The equation of motion of sandwich beam with pyramidal lattice core in the supersonic flow considering geometric nonlinearity is formulated using Hamilton＇s principle. The piston theory is used to evaluate aerodynami...The equation of motion of sandwich beam with pyramidal lattice core in the supersonic flow considering geometric nonlinearity is formulated using Hamilton＇s principle. The piston theory is used to evaluate aerodynamic pressure. The structural aeroelastic properties are analyzed using frequency- and time-domain methods, and some interesting phenomena are observed. It is noted that the flutter of sandwich beam occurs under the coupling effect of low order modes. The critical flutter aerodynamic pressure of the sandwich beam is higher than that of the isotropic beam with the same weight, length and width. The influence of inclination angle of core truss on flutter characteristic is analyzed.展开更多
In this paper, we present a strong-form framework for solving the boundary value problems with geometric nonlinearity, in which an incremental theory is developed for the problem based on the Newton-Raphson scheme. Co...In this paper, we present a strong-form framework for solving the boundary value problems with geometric nonlinearity, in which an incremental theory is developed for the problem based on the Newton-Raphson scheme. Conventionally, the finite ele- ment methods （FEMs） or weak-form based meshfree methods have often been adopted to solve geometric nonlinear problems. However, issues, such as the mesh dependency, the numerical integration, and the boundary imposition, make these approaches com- putationally inefficient. Recently, strong-form collocation methods have been called on to solve the boundary value problems. The feasibility of the collocation method with the nodal discretization such as the radial basis collocation method （RBCM） motivates the present study. Due to the limited application to the nonlinear analysis in a strong form, we formulate the equation of equilibrium, along with the boundary conditions, in an incremental-iterative sense using the RBCM. The efficacy of the proposed framework is numerically demonstrated with the solution of two benchmark problems involving the geometric nonlinearity. Compared with the conventional weak-form formulation, the pro- posed framework is advantageous as no quadrature rule is needed in constructing the governing equation, and no mesh limitation exists with the deformed geometry in the increment al-it erative process.展开更多
This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element couplin...This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element coupling stress resulting from the combination of mechanical and thermal loading,using geometric nonlinear finite element analysis.A topological model is then developed to minimize compliance while meeting displacement and frequency constraints to fulfill design requirements of structural members.Since the conventional Lagrange multiplier search method is unable to handle convergence instability arising from large deformation,a novel Lagrange multiplier search method is proposed.Additionally,the proposed method can be extended to multi-constrained geometrically nonlinear topology optimization,accommodating multiple physical field couplings.展开更多
Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an inter...Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.展开更多
Most of the previous research on concrete-filled steel tube is restricted to a deterministic approach. To gain clear insight into the random properties of circular concrete-filled steel tube, reliability analysis is c...Most of the previous research on concrete-filled steel tube is restricted to a deterministic approach. To gain clear insight into the random properties of circular concrete-filled steel tube, reliability analysis is carried out in the present study. To obtain the Structural nonlinear response and ultimate resistance capacity, material and geometrical nonlinear analysis of circular concrete-filled steel tube is performed with a three-dimensional degenerated beam ele- ment. Then we investigate the reliability of concrete-filled steel tube using the first-order reliability method combined with nonlinear finite element analysis. The influences of such parameters as material strength, slenderness, initial geo- metrical imperfection, etc. on the reliability of circular concrete-filled steel tube column are studied. It can be con- cluded that inevitable random fluctuation of those parameters has significant influence on structural reliability, and that stochastic or reliability methods can provide a more rational and subjective evaluation on the safety of CFT structures than a deterministic approach.展开更多
This paper deals with the nonlinear large deflection analysis of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates and panels using a finite element method.Based on the first-order shear deforma...This paper deals with the nonlinear large deflection analysis of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates and panels using a finite element method.Based on the first-order shear deformation theory(FSDT),the proposed model takes into account the transverse shear deformations and incorporates the geometrical nonlinearity type.A C^0 isoparametric finite shell element is developed for the present nonlinear model with the description of large displacements and finite rotations.By adopting the extended rule of mixture,the effective material properties of FG-CNTRCs are approximated with the introduction of some efficiency parameters.Four carbon nanotube(CNT)distributions,labeled uniformly distributed(UD)-CNT,FG-VCNT,FG-O-CNT,and FG-X-CNT,are considered.The solution procedure is carried out via the Newton-Raphson incremental technique.Various numerical applications in both isotropic and CNTRC composite cases are performed to trace the potential of the present model.The effects of the CNT distributions,their volume fractions,and the geometrical characteristics on the nonlinear deflection responses of FG-CNTRC structures are highlighted via a detailed parametric study.展开更多
A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order...A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order effects of element deformations, replaces the conventional incremental secant stiffness matrix. Two deformation stiffness matrices due to the variation of axial force and bending moments are included in the tangent stiffness. They are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations. A correction matrix is added to the tangent stiffness matrix to make displacement derivatives equivalent to the commutative rotational degrees of freedom. Numerical examples show that the proposed dement is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and flexural-torsional buckling, of space frames even when fewer elements are used to model a member.展开更多
This paper describes a method proposed for modeling large deflection of aircraft in nonlinear aeroelastic analysis by developing reduced order model（ROM）.The method is applied for solving the static aeroelastic and ...This paper describes a method proposed for modeling large deflection of aircraft in nonlinear aeroelastic analysis by developing reduced order model（ROM）.The method is applied for solving the static aeroelastic and static aeroelastic trim problems of flexible aircraft containing geometric nonlinearities;meanwhile,the non-planar effects of aerodynamics and follower force effect have been considered.ROMs are computational inexpensive mathematical representations compared to traditional nonlinear finite element method（FEM） especially in aeroelastic solutions.The approach for structure modeling presented here is on the basis of combined modal/finite element（MFE） method that characterizes the stiffness nonlinearities and we apply that structure modeling method as ROM to aeroelastic analysis.Moreover,the non-planar aerodynamic force is computed by the non-planar vortex lattice method（VLM）.Structure and aerodynamics can be coupled with the surface spline method.The results show that both of the static aeroelastic analysis and trim analysis of aircraft based on structure ROM can achieve a good agreement compared to analysis based on the FEM and experimental result.展开更多
The buckling behavior of single layer space structure is very sensitive. The joint rigidity, moreover, is one of the main factors of stability which may determine the entire failure behavior. Thus, the reasonable stif...The buckling behavior of single layer space structure is very sensitive. The joint rigidity, moreover, is one of the main factors of stability which may determine the entire failure behavior. Thus, the reasonable stiffness of joint system, which is neither total pin assumption nor perfect fix condition, is very important to apply to the real single layer space one. Therefore, the purpose of this work was to investigate the buckling behavior of single layer space structure, using the development of the upgraded stiffness matrix for the joint rigidity. To derive tangential stiffness matrix, a displacement function was assumed using translational and rotational displacement at the node. The geometrical nonlinear analysis was simulated not only with perfect model but also with imperfect one. As a result, the one and two free nodal numerical models were investigated using derived stiffness matrix. It was figured out that the buckling load increases in proportion to joint rigidity with rise-span ratio. The stability of numerical model is very sensitive with the initial imperfection, responding of bifurcation in the structure.展开更多
A geometrically nonlinear topology optimization method for continuum structures is proposed based on the independent continuous mapping method.The stress constraint problem is studied due to the importance of structur...A geometrically nonlinear topology optimization method for continuum structures is proposed based on the independent continuous mapping method.The stress constraint problem is studied due to the importance of structural strength in engineering applications.First,a topology optimization model is established for a lightweight structure with element stress as constraints.Second,the stress globalization method is adopted to convert local stress constraints into strain energy constraints,which overcomes the difficulties caused by local stress constraints,such as model establishment,sensitivity analysis,and massive solution calculations.Third,the sensitivity of the objective function and constraint function is analyzed,and the method of moving asymptotes is employed to solve the optimization model.In addition,the additive hyperelasticity technique is utilized to solve the numerical instability induced by structures undergoing large deformation.Numerical examples are given to validate the feasibility of the proposed method.The method provides a significant reference for geometrically nonlinear optimization design.展开更多
A geometrically nonlinear topology optimization(GNTO)method with thermal–mechanical coupling is investigated.Firstly,the new expression of element coupling stress due to superimposed mechanical and thermal loading is...A geometrically nonlinear topology optimization(GNTO)method with thermal–mechanical coupling is investigated.Firstly,the new expression of element coupling stress due to superimposed mechanical and thermal loading is obtained based on the geometrically nonlinear finite element analysis.The lightweight topology optimization(TO)model under stress constraints is established to satisfy the strength requirement.Secondly,the distortion energy theory is introduced to transform themodel into structural strain energy constraints in order to solve the implicit relationship between stress constraints and design variables.Thirdly,the sensitivity analysis of the optimization model is derived,and the model is solved by the method of moving asymptotes(MMA).Numerical examples show that temperature has a significant effect on the optimal configuration,and the TO method considering temperature load is closer to engineering design requirements.The proposed method can be extended to the GNTO design with multiple physical field coupling.展开更多
Structural shape monitoring plays a vital role in the structural health monitoring systems.The inverse finite element method(iFEM)has been demonstrated to be a practical method of deformation reconstruction owing to i...Structural shape monitoring plays a vital role in the structural health monitoring systems.The inverse finite element method(iFEM)has been demonstrated to be a practical method of deformation reconstruction owing to its unique advantages.Current iFEM formulations have been applied to small deformation of structures based on the small-displacement assumption of linear theory.However,this assumption may be inapplicable to some structures with large displacements in practical applications.Therefore,geometric nonlinearity needs to be considered.In this study,to expand the practical utility of iFEM for large displacement monitoring,we propose a nonlinear iFEM algorithm based on a four-node inverse quadrilateral shell element iQS4.Taking the advantage of an iterative iFEM algorithm,a nonlinear response is linearized to compute the geometrically nonlinear deformation reconstruction,like the basic concept of nonlinear FE analysis.Several examples are solved to verify the proposed approach.It is demonstrated that large displacements can be accurately estimated even if the in-situ sensor data includes different levels of randomly generated noise.It is proven that the nonlinear iFEM algorithm provides a more accurate displacement response as compared to the linear iFEM methodology for structures undergoing large displacement.Hence,the proposed approach can be utilized as a viable tool to effectively characterize geometrically nonlinear deformations of structures in real-time applications.展开更多
An algorithm integrating reduced order model(ROM),equivalent linearization(EL),and finite element method(FEM)is proposed to carry out geometrically nonlinear random vibration analysis of stiffened plates under acousti...An algorithm integrating reduced order model(ROM),equivalent linearization(EL),and finite element method(FEM)is proposed to carry out geometrically nonlinear random vibration analysis of stiffened plates under acoustic pressure loading.Based on large deflection finite element formulation,the nonlinear equations of motion of stiffened plates are obtained.To reduce the computation,a reduced order model of the structures is established.Then the EL technique is incorporated into FE software NASTRAN by the direct matrix abstraction program(DMAP).For the stiffened plates,a finite element model of beam and plate assembly is established,in which the nodes of beam elements are shared with shell elements,and the offset and section properties of the beam are set.The presented method can capture the root-mean-square(RMS) of the stress responses of shell and beam elements of stiffened plates,and analyze the stress distribution of the stiffened surface and the unstiffened surface,respectively.Finally,the statistical dynamic response results obtained by linear and EL methods are compared.It is shown that the proposed method can be used to analyze the geometrically nonlinear random responses of stiffened plates.The geometric nonlinearity plays an important role in the vibration response of stiffened plates,particularly at high acoustic pressure loading.展开更多
Isogeometric analysis (IGA) is known to showadvanced features compared to traditional finite element approaches.Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functiona...Isogeometric analysis (IGA) is known to showadvanced features compared to traditional finite element approaches.Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functionalgrading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward adeep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complexIGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trainedusing the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationshipbetween the outputs and the inputs is constructed usingmachine learning so that the displacements can be directlyestimated by the deep learning network. To provide enough training data, we use S-FSDT Von-Karman IGA andobtain the displacement responses for different loads and gradient indexes. Results show that the recognition erroris low, and demonstrate the feasibility of deep learning technique as a fast and accurate alternative to IGA formodeling the geometrically nonlinear bending behavior of FG plates.展开更多
A geometrically exact Kirchhoff beam formulation(GEKBF)established on the Lie group SO(3)for simulating the dynamics of a slender beam is proposed.The kinematic description,dynamic equilibrium equations and their line...A geometrically exact Kirchhoff beam formulation(GEKBF)established on the Lie group SO(3)for simulating the dynamics of a slender beam is proposed.The kinematic description,dynamic equilibrium equations and their linearization are derived in this framework.Then,a second-order interpolation function for the torsion angle is introduced to improve the convergence of the element.Next,the rotation vector parameterization is developed to reduce the geometric nonlinearity caused by the rotation of the rigid body.In addition,the influence of the reference frame is considered,and the derivation of the elastic force and Jacobian matrix is simplified using the spatial-parallel transport.The semi-discrete equations of motion are in the form of a second-order ordinary differential equation on Lie group,which are solved using the Lie group generalizedα-method.Finally,the accuracy of the proposed formulation is verified using several numerical examples.展开更多
The present study focuses on an inextensible beam and its relevant inertia nonlinearity,which are essentially distinct from the commonly treated extensible beam that is dominated by the geometric nonlinearity.Explicit...The present study focuses on an inextensible beam and its relevant inertia nonlinearity,which are essentially distinct from the commonly treated extensible beam that is dominated by the geometric nonlinearity.Explicitly,by considering a weakly constrained or free end(in the longitudinal direction),the inextensibility assumption and inertial nonlinearity(with and without an initial curvature)are introduced.For a straight beam,a multi-scale analysis of hardening/softening dynamics reveals the effects of the end stiffness/mass.Extending the straight scenario,a refined inextensible curved beam model is further proposed,accounting for both its inertial nonlinearity and geometric nonlinearity induced by the initial curvature.The numerical results for the frequency responses are also presented to illustrate the dynamic effects of the initial curvature and axial constraint,i.e.,the end mass and end stiffness.展开更多
This study presents a high-speed geometrically nonlinear flutter analysis calculation method based on the highprecision computational fluid dynamics/computational structural dynamics methods.In the proposed method,the...This study presents a high-speed geometrically nonlinear flutter analysis calculation method based on the highprecision computational fluid dynamics/computational structural dynamics methods.In the proposed method,the aerodynamic simulation was conducted based on computational fluid dynamics,and the structural model was established using the nonlinear finite element model and tangential stiffness matrix.First,the equilibrium position was obtained using the nonlinear static aeroelastic iteration.Second,the structural modal under a steady aerodynamic load was extracted.Finally,the generalized displacement time curve was obtained by coupling the unsteady aerodynamics and linearized structure motion equations.Moreover,if the flutter is not at a critical state,the incoming flow dynamic pressure needs to be changed,and the above steps must be repeated until the vibration amplitude are equal.Furthermore,the high-speed geometrically nonlinear flutter of the wing-body assemblymodel with a high-aspect ratio was investigated,and the correctness of the method was verified using high-speed wind tunnel experiments.The results showed that the geometric nonlinearity of the large deformation of the wing caused in-plane bending to become a key factor in flutter characteristics and significantly decreased the dynamic pressure and frequency of the nonlinear flutter compared to those of the linear flutter.展开更多
Based on the actual measured well depth, azimuth and oblique angles, a novel interpolation method to obtain the well axis is developed. The initial stress of drill string at the reference state consistent with well ax...Based on the actual measured well depth, azimuth and oblique angles, a novel interpolation method to obtain the well axis is developed. The initial stress of drill string at the reference state consistent with well axis can be obtained from the curvature and the tortuosity of well axis. By using the principle of virtual work, the formula to compute the equivalent load vector of the initial stress was derived. In the derivation,the natural （curvilinear） coordinate system was adopted since both the curvature and the tortuosity were generally not zero. A set of displacement functions fully reflecting the rigid body modes was used. Some basic concepts in the finite element analysis of drill string were clarified. It is hoped that the proposed method would offer a theoretical basis for handling the geometric nonlinear problem of the drill string in a 3-D larg edisplacement wellbore.展开更多
Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such a...Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.展开更多
Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficul...Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation axe imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11572007 and 11172084)
文摘The equation of motion of sandwich beam with pyramidal lattice core in the supersonic flow considering geometric nonlinearity is formulated using Hamilton＇s principle. The piston theory is used to evaluate aerodynamic pressure. The structural aeroelastic properties are analyzed using frequency- and time-domain methods, and some interesting phenomena are observed. It is noted that the flutter of sandwich beam occurs under the coupling effect of low order modes. The critical flutter aerodynamic pressure of the sandwich beam is higher than that of the isotropic beam with the same weight, length and width. The influence of inclination angle of core truss on flutter characteristic is analyzed.
基金Project supported by the Ministry of Science and Technology of Taiwan(No.MOST 104-2221-E-009-193)
文摘In this paper, we present a strong-form framework for solving the boundary value problems with geometric nonlinearity, in which an incremental theory is developed for the problem based on the Newton-Raphson scheme. Conventionally, the finite ele- ment methods （FEMs） or weak-form based meshfree methods have often been adopted to solve geometric nonlinear problems. However, issues, such as the mesh dependency, the numerical integration, and the boundary imposition, make these approaches com- putationally inefficient. Recently, strong-form collocation methods have been called on to solve the boundary value problems. The feasibility of the collocation method with the nodal discretization such as the radial basis collocation method （RBCM） motivates the present study. Due to the limited application to the nonlinear analysis in a strong form, we formulate the equation of equilibrium, along with the boundary conditions, in an incremental-iterative sense using the RBCM. The efficacy of the proposed framework is numerically demonstrated with the solution of two benchmark problems involving the geometric nonlinearity. Compared with the conventional weak-form formulation, the pro- posed framework is advantageous as no quadrature rule is needed in constructing the governing equation, and no mesh limitation exists with the deformed geometry in the increment al-it erative process.
基金supported by grants from the National Natural Science Foundation of China (51478130)the Guangzhou Municipal Education Bureau’s Scientific Research Project, China (2024312217)+1 种基金the China Scholarship Council (201808440070)the 111 Project of China (D21021).
文摘This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element coupling stress resulting from the combination of mechanical and thermal loading,using geometric nonlinear finite element analysis.A topological model is then developed to minimize compliance while meeting displacement and frequency constraints to fulfill design requirements of structural members.Since the conventional Lagrange multiplier search method is unable to handle convergence instability arising from large deformation,a novel Lagrange multiplier search method is proposed.Additionally,the proposed method can be extended to multi-constrained geometrically nonlinear topology optimization,accommodating multiple physical field couplings.
基金supported by the National Natural Science Foundation of China (50725826)Specific Research on Cable-reinforced Membranes with Super Span and Complex Single-shell Structures of Expo Axis (08dz0580303)Shanghai Postdoctoral Fund (10R21416200)
文摘Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.
基金supported by the Fundamental Research Funds for the Central Universities (SWJTU09CX012 and SWJTU11BR006)the Doctoral Fund for Youth Scholars of Ministry of Educationof China (No. 20110184120010)
文摘Most of the previous research on concrete-filled steel tube is restricted to a deterministic approach. To gain clear insight into the random properties of circular concrete-filled steel tube, reliability analysis is carried out in the present study. To obtain the Structural nonlinear response and ultimate resistance capacity, material and geometrical nonlinear analysis of circular concrete-filled steel tube is performed with a three-dimensional degenerated beam ele- ment. Then we investigate the reliability of concrete-filled steel tube using the first-order reliability method combined with nonlinear finite element analysis. The influences of such parameters as material strength, slenderness, initial geo- metrical imperfection, etc. on the reliability of circular concrete-filled steel tube column are studied. It can be con- cluded that inevitable random fluctuation of those parameters has significant influence on structural reliability, and that stochastic or reliability methods can provide a more rational and subjective evaluation on the safety of CFT structures than a deterministic approach.
文摘This paper deals with the nonlinear large deflection analysis of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates and panels using a finite element method.Based on the first-order shear deformation theory(FSDT),the proposed model takes into account the transverse shear deformations and incorporates the geometrical nonlinearity type.A C^0 isoparametric finite shell element is developed for the present nonlinear model with the description of large displacements and finite rotations.By adopting the extended rule of mixture,the effective material properties of FG-CNTRCs are approximated with the introduction of some efficiency parameters.Four carbon nanotube(CNT)distributions,labeled uniformly distributed(UD)-CNT,FG-VCNT,FG-O-CNT,and FG-X-CNT,are considered.The solution procedure is carried out via the Newton-Raphson incremental technique.Various numerical applications in both isotropic and CNTRC composite cases are performed to trace the potential of the present model.The effects of the CNT distributions,their volume fractions,and the geometrical characteristics on the nonlinear deflection responses of FG-CNTRC structures are highlighted via a detailed parametric study.
文摘A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order effects of element deformations, replaces the conventional incremental secant stiffness matrix. Two deformation stiffness matrices due to the variation of axial force and bending moments are included in the tangent stiffness. They are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations. A correction matrix is added to the tangent stiffness matrix to make displacement derivatives equivalent to the commutative rotational degrees of freedom. Numerical examples show that the proposed dement is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and flexural-torsional buckling, of space frames even when fewer elements are used to model a member.
文摘This paper describes a method proposed for modeling large deflection of aircraft in nonlinear aeroelastic analysis by developing reduced order model（ROM）.The method is applied for solving the static aeroelastic and static aeroelastic trim problems of flexible aircraft containing geometric nonlinearities;meanwhile,the non-planar effects of aerodynamics and follower force effect have been considered.ROMs are computational inexpensive mathematical representations compared to traditional nonlinear finite element method（FEM） especially in aeroelastic solutions.The approach for structure modeling presented here is on the basis of combined modal/finite element（MFE） method that characterizes the stiffness nonlinearities and we apply that structure modeling method as ROM to aeroelastic analysis.Moreover,the non-planar aerodynamic force is computed by the non-planar vortex lattice method（VLM）.Structure and aerodynamics can be coupled with the surface spline method.The results show that both of the static aeroelastic analysis and trim analysis of aircraft based on structure ROM can achieve a good agreement compared to analysis based on the FEM and experimental result.
基金Project(12 High-tech Urban C11) supported by High-tech Urban Development Program of Ministry of Land,Transport and Maritime Affairs,Korea
文摘The buckling behavior of single layer space structure is very sensitive. The joint rigidity, moreover, is one of the main factors of stability which may determine the entire failure behavior. Thus, the reasonable stiffness of joint system, which is neither total pin assumption nor perfect fix condition, is very important to apply to the real single layer space one. Therefore, the purpose of this work was to investigate the buckling behavior of single layer space structure, using the development of the upgraded stiffness matrix for the joint rigidity. To derive tangential stiffness matrix, a displacement function was assumed using translational and rotational displacement at the node. The geometrical nonlinear analysis was simulated not only with perfect model but also with imperfect one. As a result, the one and two free nodal numerical models were investigated using derived stiffness matrix. It was figured out that the buckling load increases in proportion to joint rigidity with rise-span ratio. The stability of numerical model is very sensitive with the initial imperfection, responding of bifurcation in the structure.
基金This work was supported by the National Natural Science Foundation of China(11872080)Beijing Natural Science Foundation(3192005)。
文摘A geometrically nonlinear topology optimization method for continuum structures is proposed based on the independent continuous mapping method.The stress constraint problem is studied due to the importance of structural strength in engineering applications.First,a topology optimization model is established for a lightweight structure with element stress as constraints.Second,the stress globalization method is adopted to convert local stress constraints into strain energy constraints,which overcomes the difficulties caused by local stress constraints,such as model establishment,sensitivity analysis,and massive solution calculations.Third,the sensitivity of the objective function and constraint function is analyzed,and the method of moving asymptotes is employed to solve the optimization model.In addition,the additive hyperelasticity technique is utilized to solve the numerical instability induced by structures undergoing large deformation.Numerical examples are given to validate the feasibility of the proposed method.The method provides a significant reference for geometrically nonlinear optimization design.
基金provided by the National Natural Science Foundation ofChina(Grant No.11872080)Beijing Natural Science Foundation(Grant No.3192005).
文摘A geometrically nonlinear topology optimization(GNTO)method with thermal–mechanical coupling is investigated.Firstly,the new expression of element coupling stress due to superimposed mechanical and thermal loading is obtained based on the geometrically nonlinear finite element analysis.The lightweight topology optimization(TO)model under stress constraints is established to satisfy the strength requirement.Secondly,the distortion energy theory is introduced to transform themodel into structural strain energy constraints in order to solve the implicit relationship between stress constraints and design variables.Thirdly,the sensitivity analysis of the optimization model is derived,and the model is solved by the method of moving asymptotes(MMA).Numerical examples show that temperature has a significant effect on the optimal configuration,and the TO method considering temperature load is closer to engineering design requirements.The proposed method can be extended to the GNTO design with multiple physical field coupling.
基金supported by the NationalNatural Science Foundation of China(Grant No.11902253)the Fundamental Research Funds for the Central Universities of China.The authors are grateful for this support.
文摘Structural shape monitoring plays a vital role in the structural health monitoring systems.The inverse finite element method(iFEM)has been demonstrated to be a practical method of deformation reconstruction owing to its unique advantages.Current iFEM formulations have been applied to small deformation of structures based on the small-displacement assumption of linear theory.However,this assumption may be inapplicable to some structures with large displacements in practical applications.Therefore,geometric nonlinearity needs to be considered.In this study,to expand the practical utility of iFEM for large displacement monitoring,we propose a nonlinear iFEM algorithm based on a four-node inverse quadrilateral shell element iQS4.Taking the advantage of an iterative iFEM algorithm,a nonlinear response is linearized to compute the geometrically nonlinear deformation reconstruction,like the basic concept of nonlinear FE analysis.Several examples are solved to verify the proposed approach.It is demonstrated that large displacements can be accurately estimated even if the in-situ sensor data includes different levels of randomly generated noise.It is proven that the nonlinear iFEM algorithm provides a more accurate displacement response as compared to the linear iFEM methodology for structures undergoing large displacement.Hence,the proposed approach can be utilized as a viable tool to effectively characterize geometrically nonlinear deformations of structures in real-time applications.
基金supported by the National Natural Science Foundations of China(Nos.11872079,11572109)the Science and Technology Project of Hebei Education Department(No.QN2019135)Advanced Talents Incubation Program of the Hebei University(No.521000981285)。
文摘An algorithm integrating reduced order model(ROM),equivalent linearization(EL),and finite element method(FEM)is proposed to carry out geometrically nonlinear random vibration analysis of stiffened plates under acoustic pressure loading.Based on large deflection finite element formulation,the nonlinear equations of motion of stiffened plates are obtained.To reduce the computation,a reduced order model of the structures is established.Then the EL technique is incorporated into FE software NASTRAN by the direct matrix abstraction program(DMAP).For the stiffened plates,a finite element model of beam and plate assembly is established,in which the nodes of beam elements are shared with shell elements,and the offset and section properties of the beam are set.The presented method can capture the root-mean-square(RMS) of the stress responses of shell and beam elements of stiffened plates,and analyze the stress distribution of the stiffened surface and the unstiffened surface,respectively.Finally,the statistical dynamic response results obtained by linear and EL methods are compared.It is shown that the proposed method can be used to analyze the geometrically nonlinear random responses of stiffened plates.The geometric nonlinearity plays an important role in the vibration response of stiffened plates,particularly at high acoustic pressure loading.
基金the National Natural Science Foundation of China(NSFC)under Grant Nos.12272124 and 11972146.
文摘Isogeometric analysis (IGA) is known to showadvanced features compared to traditional finite element approaches.Using IGA one may accurately obtain the geometrically nonlinear bending behavior of plates with functionalgrading (FG). However, the procedure is usually complex and often is time-consuming. We thus put forward adeep learning method to model the geometrically nonlinear bending behavior of FG plates, bypassing the complexIGA simulation process. A long bidirectional short-term memory (BLSTM) recurrent neural network is trainedusing the load and gradient index as inputs and the displacement responses as outputs. The nonlinear relationshipbetween the outputs and the inputs is constructed usingmachine learning so that the displacements can be directlyestimated by the deep learning network. To provide enough training data, we use S-FSDT Von-Karman IGA andobtain the displacement responses for different loads and gradient indexes. Results show that the recognition erroris low, and demonstrate the feasibility of deep learning technique as a fast and accurate alternative to IGA formodeling the geometrically nonlinear bending behavior of FG plates.
基金the National Natural Science Foundation of China(Grant Nos.12102033,12072026,and 11832005).
文摘A geometrically exact Kirchhoff beam formulation(GEKBF)established on the Lie group SO(3)for simulating the dynamics of a slender beam is proposed.The kinematic description,dynamic equilibrium equations and their linearization are derived in this framework.Then,a second-order interpolation function for the torsion angle is introduced to improve the convergence of the element.Next,the rotation vector parameterization is developed to reduce the geometric nonlinearity caused by the rotation of the rigid body.In addition,the influence of the reference frame is considered,and the derivation of the elastic force and Jacobian matrix is simplified using the spatial-parallel transport.The semi-discrete equations of motion are in the form of a second-order ordinary differential equation on Lie group,which are solved using the Lie group generalizedα-method.Finally,the accuracy of the proposed formulation is verified using several numerical examples.
基金Project supported by the National Natural Science Foundation of China(Nos.12372007,12432001,12372006,and 11972151)。
文摘The present study focuses on an inextensible beam and its relevant inertia nonlinearity,which are essentially distinct from the commonly treated extensible beam that is dominated by the geometric nonlinearity.Explicitly,by considering a weakly constrained or free end(in the longitudinal direction),the inextensibility assumption and inertial nonlinearity(with and without an initial curvature)are introduced.For a straight beam,a multi-scale analysis of hardening/softening dynamics reveals the effects of the end stiffness/mass.Extending the straight scenario,a refined inextensible curved beam model is further proposed,accounting for both its inertial nonlinearity and geometric nonlinearity induced by the initial curvature.The numerical results for the frequency responses are also presented to illustrate the dynamic effects of the initial curvature and axial constraint,i.e.,the end mass and end stiffness.
文摘This study presents a high-speed geometrically nonlinear flutter analysis calculation method based on the highprecision computational fluid dynamics/computational structural dynamics methods.In the proposed method,the aerodynamic simulation was conducted based on computational fluid dynamics,and the structural model was established using the nonlinear finite element model and tangential stiffness matrix.First,the equilibrium position was obtained using the nonlinear static aeroelastic iteration.Second,the structural modal under a steady aerodynamic load was extracted.Finally,the generalized displacement time curve was obtained by coupling the unsteady aerodynamics and linearized structure motion equations.Moreover,if the flutter is not at a critical state,the incoming flow dynamic pressure needs to be changed,and the above steps must be repeated until the vibration amplitude are equal.Furthermore,the high-speed geometrically nonlinear flutter of the wing-body assemblymodel with a high-aspect ratio was investigated,and the correctness of the method was verified using high-speed wind tunnel experiments.The results showed that the geometric nonlinearity of the large deformation of the wing caused in-plane bending to become a key factor in flutter characteristics and significantly decreased the dynamic pressure and frequency of the nonlinear flutter compared to those of the linear flutter.
文摘Based on the actual measured well depth, azimuth and oblique angles, a novel interpolation method to obtain the well axis is developed. The initial stress of drill string at the reference state consistent with well axis can be obtained from the curvature and the tortuosity of well axis. By using the principle of virtual work, the formula to compute the equivalent load vector of the initial stress was derived. In the derivation,the natural （curvilinear） coordinate system was adopted since both the curvature and the tortuosity were generally not zero. A set of displacement functions fully reflecting the rigid body modes was used. Some basic concepts in the finite element analysis of drill string were clarified. It is hoped that the proposed method would offer a theoretical basis for handling the geometric nonlinear problem of the drill string in a 3-D larg edisplacement wellbore.
基金supported by the National Science Fund for Distinguished Young Scholars (No. 50725826).
文摘Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.
基金Project supported by the National 973 Program (No.2004CB719402), the National Natural Science Foundation of China (No. 10372030)the Open Research Projects supported by the Project Fund of the Hubei Province Key Lab of Mechanical Transmission & Manufacturing Engineering Wuhan University of Science & Technology (No.2003A16).
文摘Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation axe imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.
