Curved beams with complex geometries are vital in numerous engineering applications,where precise vibration analysis is crucial for ensuring safe and effective designs.Traditional finite element methods(FEMs) often st...Curved beams with complex geometries are vital in numerous engineering applications,where precise vibration analysis is crucial for ensuring safe and effective designs.Traditional finite element methods(FEMs) often struggle to accurately represent the dynamic characteristics of these structures due to the limitations in their shape function approximations.To overcome this challenge,the current study introduces an innovative finite element(FE)-based technique for the undamped vibrational analysis of curved beams with arbitrary curvature,employing explicitly derived interpolation functions.Initially,the exact interpolation functions are developed for circular are elements with the force method.These functions facilitate the creation of a highly accurate stiffness matrix,which is validated against the benchmark examples.To accommodate arbitrary curvature,a systematic transformation technique is established to approximate the intricate curves with a series of circular arcs.The numerical findings indicate that increasing the number of arc segments enhances accuracy,approaching the exact solutions.The analysis of free vibrations is conducted for both circular and non-circular beams.Mass matrices are derived using two methods:lumped mass and consistent mass,where the latter is based on the interpolation functions.The effectiveness of the proposed method is confirmed through the comparisons with the existing literature,demonstrating strong agreement.Finally,several practical cases involving beams with diverse curvature profiles are analyzed.Both natural frequencies and mode shapes are determined,providing significant insights into the dynamic behavior of these structures.This research offers a dependable and efficient analytical framework for the vibrational analysis of complex curved beams,with promising implications for structural and mechanical engineering.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
This work was to reveal the residual stress profile in electron beam welded Ti-6Al-4V alloy plates（50 mm thick） by using finite element and contour measurement methods.A three-dimensional finite element model of 50-...This work was to reveal the residual stress profile in electron beam welded Ti-6Al-4V alloy plates（50 mm thick） by using finite element and contour measurement methods.A three-dimensional finite element model of 50-mmthick titanium component was proposed,in which a column–cone combined heat source model was used to simulate the temperature field and a thermo-elastic–plastic model to analyze residual stress in a weld joint based on ABAQUS software.Considering the uncertainty of welding simulation,the computation was calibrated by experimental data of contour measurement method.Both test and simulated results show that residual stresses on the surface and inside the weld zone are significantly different and present a narrow and large gradient feature in the weld joint.The peak tensile stress exceeds the yield strength of base materials inside weld,which are distinctly different from residual stress of the thin Ti-6Al-4V alloy plates presented in references before.展开更多
A three-dimensional finite-element model (FEM) used for calculating electron beam (EB) welding temperature and stresses fields of thin plates of BT20 titanium has been developed in which the nonlinear thermophysical a...A three-dimensional finite-element model (FEM) used for calculating electron beam (EB) welding temperature and stresses fields of thin plates of BT20 titanium has been developed in which the nonlinear thermophysical and thermo-mechanical properties of the material has been considered. The welding temperature field, the distributions of residual stresses in as-welded (AW) and electron beam local post-weld heat treatment (EBLPWHT) conditions have been successfully simulated. The results show that: (1) In the weld center, the maximum magnitude of residual tensile stresses of BT20 thin plates of Ti alloy is equal to 60%- 70% of its yield strength σs. (2) The residual tensile stresses in weld center can be even decreased after EBLPWHT and the longitudinal tensile stresses are decreased about 50% compared to joints in AW conditions. (3) The numerical calculating results of residual stresses by using FEM are basically in agreement with the experimental results. Combined with numerical calculating results, the effects of electron beam welding and EBLPWHT on the distribution of welding residual stresses in thin plates of BT20 have been analyzed in detail.展开更多
A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces...A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.展开更多
Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the...Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.展开更多
A fiber-section model based Timoshenko beam element is proposed in this study that is founded on the nonlinear analysis of frame elements considering axial, flexural, and shear deformations. This model is achieved usi...A fiber-section model based Timoshenko beam element is proposed in this study that is founded on the nonlinear analysis of frame elements considering axial, flexural, and shear deformations. This model is achieved using a shear-bending interdependent formulation （SBIF）. The shape function of the element is derived from the exact solution of the homogeneous form of the equilibrium equation for the Timoshenko deformation hypothesis.The proposed element is free from shear-locking. The sectional fiber model is constituted with a multi-axial plasticity material model, which is used to simulate the coupled shear-axial nonlinear behavior of each fiber. By imposing deformation compatibility conditions among the fibers, the sectional and elemental resisting forces are calculated. Since the SBIF shape functions are interactive with the shear-corrector factor for different shapes of sections, an iterative procedure is introduced in the nonlinear state determination of the proposed Timoshenko element. In addition, the proposed model tackles the geometric nonlinear problem by adopting a corotational coordinate transformation approach. The derivation procedure of the corotational algorithm of the SBIF Timoshenko element for nonlinear geometrical analysis is presented. Numerical examples confirm that the SBIF Timoshenko element with a fiber-section model has the same accuracy and robustness as the flexibility-based formulation. Finally, the SBIF Timoshenko element is extended and demonstratedin a three-dimensional numerical example.展开更多
Combined multi-body dynamics with structural dynamics, a new discrete element with flexible connector, which is applicable for 3-D beam structures, is developed in this paper. Both the generalized elastic coefficient ...Combined multi-body dynamics with structural dynamics, a new discrete element with flexible connector, which is applicable for 3-D beam structures, is developed in this paper. Both the generalized elastic coefficient matrix of the flexible connector and the mass matrix of discrete element may be off-diagonal in a general case. The zero-length rigid element is introduced to simulate the node at which multiple elements are jointed together. It may also be effective when the axes of adjacent elements are not in the same line. The examples for eigenvalue calculation show that the model is successful. It can be extended to the geometric nonlinear response analysis.展开更多
Diffractive optical elements（DOEs） with spectrum separation and beam concentration（SSBC） functions have important applications in solar cell systems. With the SSBC DOEs, the sunlight radiation is divided into seve...Diffractive optical elements（DOEs） with spectrum separation and beam concentration（SSBC） functions have important applications in solar cell systems. With the SSBC DOEs, the sunlight radiation is divided into several wave bands so as to be effectively absorbed by photovoltaic materials with different band gaps. A new method is proposed for designing high-efficiency SSBC DOEs, which is physically simple, numerically fast, and universally applicable. The SSBC DOEs are designed by the new design method, and their performances are analyzed by the Fresnel diffraction integral method.The new design method takes two advantages over the previous design method. Firstly, the optical focusing efficiency is heightened by up to 10%. Secondly, focal positions of all the designed wavelengths can be designated arbitrarily and independently. It is believed that the designed SSBC DOEs should have practical applications to solar cell systems.展开更多
Slip of a composite box beam may reduce its stiffness, enlarge its deformation and affect its performance. In this work, the governing differential equations and boundary conditions of composite box beams were establi...Slip of a composite box beam may reduce its stiffness, enlarge its deformation and affect its performance. In this work, the governing differential equations and boundary conditions of composite box beams were established. Analytic solutions of combined differential equations were also established. Partial degree of freedom was adopted to establish a new FEA element of three-dimensional beam, taking into account the slip effect. Slip and its first-order derivative were introduced into the nodes of composite box beams as generalized degree of freedom. Stiffness matrix and load array of beam elements were established. A three-dimensional nonlinear calculation program was worked out. The results show that the element is reliable and easy to divide and is suitable for special nonlinear analysis of large-span composite box beams.展开更多
In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. ...In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces. The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics. Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion. Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method. It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method. Further, envelopes of resultant forces which are of primary importance for the purpose of design, are developed for a given ground motion at the end.展开更多
The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were der...The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given.Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions.The EEP method gives super_convergent nodal stresses,which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude.And in addition,it can overcome the “shear locking” difficulty for stresses even when the displacements are badly affected.This research paves the way for application of the EEP method to general one_dimensional systems of ordinary differential equations.展开更多
A thermomechanical model of a shape memory alloy beam bending under tip force loading is implemented in finite element codes.The constitutive model is a one dimensional model which is based on free energy and motivate...A thermomechanical model of a shape memory alloy beam bending under tip force loading is implemented in finite element codes.The constitutive model is a one dimensional model which is based on free energy and motivated by statistical thermodynamics.The particular focus of this paper is on the aspects of finite element modeling and simulation of the inhomogeneous beam bending problem.This paper extends previous work which is based on the small deformation Euler-Bernoulli beam theory and by treating an SMA beam as consisting of multi-layers in a twodimensional model.The flux terms are involved in the heat transfer equation.The simulations can represent both shape memory effect and super-elastic behavior.Different thermal boundary condition effect and load rate effect can also be captured.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
The temperature and stress profiles of porous cubic Ti-6Al-4V titanium alloy grids by additive manufacturing via electron beam melting(EBM)based on finite element(FE)method were investigated.Three-dimensional FE model...The temperature and stress profiles of porous cubic Ti-6Al-4V titanium alloy grids by additive manufacturing via electron beam melting(EBM)based on finite element(FE)method were investigated.Three-dimensional FE models were developed to simulate the single-layer and five-layer girds under annular and lateral scanning.The results showed that the molten pool temperature in five-layer girds was higher than that in single-layer grids owing to the larger mass and higher heat capacity.More energies accumulated by the longer scanning time for annular path than lateral path led to the higher temperature and steeper temperature gradient.The thermal stress drastically fluctuated during EBM process and the residual stress decreased with the increase of powder layer where the largest stress appeared at the first layer along the build direction.The stress under lateral scanning was slightly larger but relatively more homogeneous distribution than those under annular scanning.The stress distribution showed anisotropy and the maximum Von Mises stress occurred around the central node.The stress profiles were explained by the temperature fields and grids structure.展开更多
Piezoelectric bender elements are widely used as electromechanical sensors and actuators, An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation th...Piezoelectric bender elements are widely used as electromechanical sensors and actuators, An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory （FSDT）, which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers, and corrects the effect of transverse shear strain on the electric displacement integration. Free vibration analysis of simplysupported bender elements was carried out and the numerical results showed that, solutions of the present model for various thickness-to-length ratios are compared well with the exact two-dimensional solutions, which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.展开更多
Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained result...Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.展开更多
In this work,a three-dimensional nonlinear transient thermo-mechanically coupled finite element model(FEM)is established to investigate the variation in temperature and stress fields during electron beam melting(EBM)o...In this work,a three-dimensional nonlinear transient thermo-mechanically coupled finite element model(FEM)is established to investigate the variation in temperature and stress fields during electron beam melting(EBM)of rhombic dodecahedron Ti-6Al-4V alloy.The influence of the processing parameters on the temperature and residual stress evolutions was predicted and verified against existing literature data.The calculated results indicate that the interlayer cooling time has very little effect on both the temperature and stress evolutions,indicating that the interlayer cooling time can be set up as short as possible to reduce manufacturing time.It is presented that the residual stress of the intersection is higher than that of non-intersection.With increasing preheating temperature,the residual stress decreases continuously,which is about 20%–30%for every 50℃rise in temperature.The temperature and stress fields repeated every four layers with the complex periodic scanning strategy.Both x and y-component residual stresses are tensile stresses,while z-component stress is weak compressive or tensile stress in typical paths.It is proposed that the interlayer cooling is necessary to obtain a rhombic dodecahedron with low residual stress.These results can bring insights into the understanding of the residual stress during EBM.展开更多
A tensor-based updated Lagrangian （UL） formulation for the geometrically nonlinear analysis of 2D beam-column structures is developed by using curvilinear coordinates, which has considered the effects of the deforme...A tensor-based updated Lagrangian （UL） formulation for the geometrically nonlinear analysis of 2D beam-column structures is developed by using curvilinear coordinates, which has considered the effects of the deformed curvature. Between the known configuration C1 and the desired configuration C2, a configuration C2^＊ derived by rigid-body motion of C1 is introduced to eliminate the element-end transverse displacements between C2^＊ and C2. A stiffness matrix is obtained in C2^＊; and then by a transformation defined by the element-end displacements, the stiffness matrix in C2^＊ is transformed into that in CI. Comparing the stiffness matrix with that in the conventional UL formulation for a 2D beam element, the initial displacement stiffness matrix emerges, which results from the deformed curvature within the element. Numerical examples have verified the accuracy and efficiency of the present formulation, and the results show that the deformed curvatures have significant effects when deformations are large.展开更多
文摘Curved beams with complex geometries are vital in numerous engineering applications,where precise vibration analysis is crucial for ensuring safe and effective designs.Traditional finite element methods(FEMs) often struggle to accurately represent the dynamic characteristics of these structures due to the limitations in their shape function approximations.To overcome this challenge,the current study introduces an innovative finite element(FE)-based technique for the undamped vibrational analysis of curved beams with arbitrary curvature,employing explicitly derived interpolation functions.Initially,the exact interpolation functions are developed for circular are elements with the force method.These functions facilitate the creation of a highly accurate stiffness matrix,which is validated against the benchmark examples.To accommodate arbitrary curvature,a systematic transformation technique is established to approximate the intricate curves with a series of circular arcs.The numerical findings indicate that increasing the number of arc segments enhances accuracy,approaching the exact solutions.The analysis of free vibrations is conducted for both circular and non-circular beams.Mass matrices are derived using two methods:lumped mass and consistent mass,where the latter is based on the interpolation functions.The effectiveness of the proposed method is confirmed through the comparisons with the existing literature,demonstrating strong agreement.Finally,several practical cases involving beams with diverse curvature profiles are analyzed.Both natural frequencies and mode shapes are determined,providing significant insights into the dynamic behavior of these structures.This research offers a dependable and efficient analytical framework for the vibrational analysis of complex curved beams,with promising implications for structural and mechanical engineering.
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supported by the National Natural Science Foundation of China (No.50935008)
文摘This work was to reveal the residual stress profile in electron beam welded Ti-6Al-4V alloy plates（50 mm thick） by using finite element and contour measurement methods.A three-dimensional finite element model of 50-mmthick titanium component was proposed,in which a column–cone combined heat source model was used to simulate the temperature field and a thermo-elastic–plastic model to analyze residual stress in a weld joint based on ABAQUS software.Considering the uncertainty of welding simulation,the computation was calibrated by experimental data of contour measurement method.Both test and simulated results show that residual stresses on the surface and inside the weld zone are significantly different and present a narrow and large gradient feature in the weld joint.The peak tensile stress exceeds the yield strength of base materials inside weld,which are distinctly different from residual stress of the thin Ti-6Al-4V alloy plates presented in references before.
文摘A three-dimensional finite-element model (FEM) used for calculating electron beam (EB) welding temperature and stresses fields of thin plates of BT20 titanium has been developed in which the nonlinear thermophysical and thermo-mechanical properties of the material has been considered. The welding temperature field, the distributions of residual stresses in as-welded (AW) and electron beam local post-weld heat treatment (EBLPWHT) conditions have been successfully simulated. The results show that: (1) In the weld center, the maximum magnitude of residual tensile stresses of BT20 thin plates of Ti alloy is equal to 60%- 70% of its yield strength σs. (2) The residual tensile stresses in weld center can be even decreased after EBLPWHT and the longitudinal tensile stresses are decreased about 50% compared to joints in AW conditions. (3) The numerical calculating results of residual stresses by using FEM are basically in agreement with the experimental results. Combined with numerical calculating results, the effects of electron beam welding and EBLPWHT on the distribution of welding residual stresses in thin plates of BT20 have been analyzed in detail.
基金The project supported by the National Natural Science Foundation of China(10172023)
文摘A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.
基金supported by the National Natural Science Foundation of China(10872126)Research Fund for the Doctoral Program of Higher Education of China(20100073110007)
文摘Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.
基金National Program on Key Basic Research Project of China (973) under Grant No.2011CB013603National Natural Science Foundation of China under Grant Nos.51008208,51378341+1 种基金Projects International Cooperation and Exchanges NSFC (NSFC-JST) under Grant No.51021140003Tianjin Municipal Natural Science Foundation under Grant No.13JCQNJC07200
文摘A fiber-section model based Timoshenko beam element is proposed in this study that is founded on the nonlinear analysis of frame elements considering axial, flexural, and shear deformations. This model is achieved using a shear-bending interdependent formulation （SBIF）. The shape function of the element is derived from the exact solution of the homogeneous form of the equilibrium equation for the Timoshenko deformation hypothesis.The proposed element is free from shear-locking. The sectional fiber model is constituted with a multi-axial plasticity material model, which is used to simulate the coupled shear-axial nonlinear behavior of each fiber. By imposing deformation compatibility conditions among the fibers, the sectional and elemental resisting forces are calculated. Since the SBIF shape functions are interactive with the shear-corrector factor for different shapes of sections, an iterative procedure is introduced in the nonlinear state determination of the proposed Timoshenko element. In addition, the proposed model tackles the geometric nonlinear problem by adopting a corotational coordinate transformation approach. The derivation procedure of the corotational algorithm of the SBIF Timoshenko element for nonlinear geometrical analysis is presented. Numerical examples confirm that the SBIF Timoshenko element with a fiber-section model has the same accuracy and robustness as the flexibility-based formulation. Finally, the SBIF Timoshenko element is extended and demonstratedin a three-dimensional numerical example.
基金The project was financially supported by the National Natural Science Foundation of China
文摘Combined multi-body dynamics with structural dynamics, a new discrete element with flexible connector, which is applicable for 3-D beam structures, is developed in this paper. Both the generalized elastic coefficient matrix of the flexible connector and the mass matrix of discrete element may be off-diagonal in a general case. The zero-length rigid element is introduced to simulate the node at which multiple elements are jointed together. It may also be effective when the axes of adjacent elements are not in the same line. The examples for eigenvalue calculation show that the model is successful. It can be extended to the geometric nonlinear response analysis.
基金Project supported by the National Basic Research Program of China(Grant No.2013CBA01702)the National Natural Science Foundation of China(Grant Nos.11474206,91233202,11374216,and 11404224)+1 种基金the Scientific Research Project of Beijing Education Commission,China(Grant No.KM201310028005)the Scientific Research Base Development Program of the Beijing Municipal Commission of Education and the Beijing Youth Top-Notch Talent Training Plan,China(Grant No.CIT&TCD201504080)
文摘Diffractive optical elements（DOEs） with spectrum separation and beam concentration（SSBC） functions have important applications in solar cell systems. With the SSBC DOEs, the sunlight radiation is divided into several wave bands so as to be effectively absorbed by photovoltaic materials with different band gaps. A new method is proposed for designing high-efficiency SSBC DOEs, which is physically simple, numerically fast, and universally applicable. The SSBC DOEs are designed by the new design method, and their performances are analyzed by the Fresnel diffraction integral method.The new design method takes two advantages over the previous design method. Firstly, the optical focusing efficiency is heightened by up to 10%. Secondly, focal positions of all the designed wavelengths can be designated arbitrarily and independently. It is believed that the designed SSBC DOEs should have practical applications to solar cell systems.
基金Project(50708112) supported by the National Natural Science Foundation of ChinaProject(IRT1296) supported by the Program for Changjiang Scholars and Innovative Research Team in University
文摘Slip of a composite box beam may reduce its stiffness, enlarge its deformation and affect its performance. In this work, the governing differential equations and boundary conditions of composite box beams were established. Analytic solutions of combined differential equations were also established. Partial degree of freedom was adopted to establish a new FEA element of three-dimensional beam, taking into account the slip effect. Slip and its first-order derivative were introduced into the nodes of composite box beams as generalized degree of freedom. Stiffness matrix and load array of beam elements were established. A three-dimensional nonlinear calculation program was worked out. The results show that the element is reliable and easy to divide and is suitable for special nonlinear analysis of large-span composite box beams.
文摘In this study, a new method for conversion of solid finite element solution to beam finite element solution is developed based on the meta-modeling theory which constructs a model consistent with continuum mechanics. The proposed method is rigorous and efficient compared to a typical conversion method which merely computes surface integration of solid element nodal stresses to obtain cross-sectional forces. The meta-modeling theory ensures the rigorousness of proposed method by defining a proper distance between beam element and solid element solutions in a function space of continuum mechanics. Results of numerical verification test that is conducted with a simple cantilever beam are used to find the proper distance function for this conversion. Time history analysis of the main tunnel structure of a real ramp tunnel is considered as a numerical example for the proposed conversion method. It is shown that cross-sectional forces are readily computed for solid element solution of the main tunnel structure when it is converted to a beam element solution using the proposed method. Further, envelopes of resultant forces which are of primary importance for the purpose of design, are developed for a given ground motion at the end.
文摘The newly proposed element energy projection(EEP) method has been applied to the computation of super_convergent nodal stresses of Timoshenko beam elements.General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given.Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions.The EEP method gives super_convergent nodal stresses,which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude.And in addition,it can overcome the “shear locking” difficulty for stresses even when the displacements are badly affected.This research paves the way for application of the EEP method to general one_dimensional systems of ordinary differential equations.
文摘A thermomechanical model of a shape memory alloy beam bending under tip force loading is implemented in finite element codes.The constitutive model is a one dimensional model which is based on free energy and motivated by statistical thermodynamics.The particular focus of this paper is on the aspects of finite element modeling and simulation of the inhomogeneous beam bending problem.This paper extends previous work which is based on the small deformation Euler-Bernoulli beam theory and by treating an SMA beam as consisting of multi-layers in a twodimensional model.The flux terms are involved in the heat transfer equation.The simulations can represent both shape memory effect and super-elastic behavior.Different thermal boundary condition effect and load rate effect can also be captured.
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The work was financially supported by the Natural Science Foundation of Shandong Province,China(No.ZR2019MEM012)the Major Scientific and Technological Innovation Program of Shandong Province,China(No.2019JZZY010325)+1 种基金the Key Research Program of Frontier Sciences,CAS(No.QYZDJ-SSW-JSC031-02)the National Natural Science Foundation of China(No.51871220).
文摘The temperature and stress profiles of porous cubic Ti-6Al-4V titanium alloy grids by additive manufacturing via electron beam melting(EBM)based on finite element(FE)method were investigated.Three-dimensional FE models were developed to simulate the single-layer and five-layer girds under annular and lateral scanning.The results showed that the molten pool temperature in five-layer girds was higher than that in single-layer grids owing to the larger mass and higher heat capacity.More energies accumulated by the longer scanning time for annular path than lateral path led to the higher temperature and steeper temperature gradient.The thermal stress drastically fluctuated during EBM process and the residual stress decreased with the increase of powder layer where the largest stress appeared at the first layer along the build direction.The stress under lateral scanning was slightly larger but relatively more homogeneous distribution than those under annular scanning.The stress distribution showed anisotropy and the maximum Von Mises stress occurred around the central node.The stress profiles were explained by the temperature fields and grids structure.
基金the National Natural Science Foundation of China(No.10472102)theNational Basic Research Program of China(No.2007CB714200)
文摘Piezoelectric bender elements are widely used as electromechanical sensors and actuators, An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory （FSDT）, which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers, and corrects the effect of transverse shear strain on the electric displacement integration. Free vibration analysis of simplysupported bender elements was carried out and the numerical results showed that, solutions of the present model for various thickness-to-length ratios are compared well with the exact two-dimensional solutions, which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.
文摘Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.
基金supported by the Natural Science Foundation of Shandong Province,China(No.ZR2019MEM012).
文摘In this work,a three-dimensional nonlinear transient thermo-mechanically coupled finite element model(FEM)is established to investigate the variation in temperature and stress fields during electron beam melting(EBM)of rhombic dodecahedron Ti-6Al-4V alloy.The influence of the processing parameters on the temperature and residual stress evolutions was predicted and verified against existing literature data.The calculated results indicate that the interlayer cooling time has very little effect on both the temperature and stress evolutions,indicating that the interlayer cooling time can be set up as short as possible to reduce manufacturing time.It is presented that the residual stress of the intersection is higher than that of non-intersection.With increasing preheating temperature,the residual stress decreases continuously,which is about 20%–30%for every 50℃rise in temperature.The temperature and stress fields repeated every four layers with the complex periodic scanning strategy.Both x and y-component residual stresses are tensile stresses,while z-component stress is weak compressive or tensile stress in typical paths.It is proposed that the interlayer cooling is necessary to obtain a rhombic dodecahedron with low residual stress.These results can bring insights into the understanding of the residual stress during EBM.
文摘A tensor-based updated Lagrangian （UL） formulation for the geometrically nonlinear analysis of 2D beam-column structures is developed by using curvilinear coordinates, which has considered the effects of the deformed curvature. Between the known configuration C1 and the desired configuration C2, a configuration C2^＊ derived by rigid-body motion of C1 is introduced to eliminate the element-end transverse displacements between C2^＊ and C2. A stiffness matrix is obtained in C2^＊; and then by a transformation defined by the element-end displacements, the stiffness matrix in C2^＊ is transformed into that in CI. Comparing the stiffness matrix with that in the conventional UL formulation for a 2D beam element, the initial displacement stiffness matrix emerges, which results from the deformed curvature within the element. Numerical examples have verified the accuracy and efficiency of the present formulation, and the results show that the deformed curvatures have significant effects when deformations are large.
