This paper discusses the elastic equilibrium problems of anisotropic skew thin plate of variable thickness simply supported on all four sides in nonlinear theories, and uses the Navier method to seek an approach to th...This paper discusses the elastic equilibrium problems of anisotropic skew thin plate of variable thickness simply supported on all four sides in nonlinear theories, and uses the Navier method to seek an approach to the problem, and to illustrate the solution with the examples. In conclusion, the mention is made of the scope of application and the convergency of the solution.展开更多
Recent engineering applications increasingly adopt smart materials,whose mechanical responses are sensitive to magnetic and electric fields.In this context,new and computationally efficient modeling strategies are ess...Recent engineering applications increasingly adopt smart materials,whose mechanical responses are sensitive to magnetic and electric fields.In this context,new and computationally efficient modeling strategies are essential to predict the multiphysic behavior of advanced structures accurately.Therefore,the manuscript presents a higher-order formulation for the static analysis of laminated anisotropic magneto-electro-elastic doubly-curved shell structures.The fundamental relations account for the full coupling between the electric field,magnetic field,and mechanical elasticity.The configuration variables are expanded along the thickness direction using a generalized formulation based on the Equivalent Layer-Wise approach.Higher-order polynomials are selected,allowing for the assessment of prescribed values of the configuration variables at the top and bottom sides of solids.In addition,an effective strategy is provided for modeling general surface distributions of mechanical pressures and electromagnetic external fluxes.The model is based on a continuum-based formulation which employs an analytical homogenization of the multifield material properties,based on Mori&Tanaka approach,of a magneto-electro-elastic composite material obtained from a piezoelectric and a piezomagnetic phase,with coupled magneto-electro-elastic effects.A semi-analytical Navier solution is applied to the fundamental equations,and an efficient post-processing equilibrium-based procedure is here used,based on the numerical assessment with the Generalized Differential Quadrature(GDQ)method,to recover the response of three-dimensional shells.The formulation is validated through various examples,investigating the multifield response of panels of different curvatures and lamination schemes.An efficient homogenization procedure,based on the Mori&Tanaka approach,is employed to obtain the three-dimensional constitutive relation of magneto-electro-elastic materials.Each model is validated against three-dimensional finite-element simulations,as developed in commercial codes.Furthermore,the full coupling effect between the electric and magnetic response is evaluated via a parametric investigation,with useful insights for design purposes of many engineering applications.The paper,thus,provides a formulation for the magneto-electro-elastic analysis of laminated structures,with a high computational efficiency,since it provides results with three-dimensional capabilities with a two-dimensional formulation.The adoption of higher-order theories,indeed,allows us to efficiently predict not only the mechanical response of the structure as happens in existing literature,but also the through-the-thickness distribution of electric and magnetic variables.A novel higher-order theory has been proposed in this work for the magneto-electro-elastic analysis of laminated shell structures with varying curvatures.This theory employs a generalized method to model the distribution of the displacement field components,electrostatic,and magneto-static potential,accounting for higher-order polynomials.The thickness functions have been defined to prescribe the arbitrary values of configuration variables at the top and bottom surfaces,even though the model is ESL-based.The fundamental governing equations have been derived in curvilinear principal coordinates,considering all coupling effects among different physical phenomena,including piezoelectric,piezomagnetic,and magneto-electric effects.A homogenization algorithm based on a Mori&Tanaka approach has been adopted to obtain the equivalent magneto-electro-mechanical properties of a two-phase transversely isotropic composite.In addition,an effective method has been adopted involving the external loads in terms of surface tractions,as well as the electric and magnetic fluxes.In the post-processing stage,a GDQ-based procedure provides the actual 3D response of a doubly-curved solid.The model has been validated through significant numerical examples,showing that the results of this semi-analytical theory align well with those obtained from 3D numerical models from commercial codes.In particular,the accuracy of the model has been verified for lamination schemes with soft layers and various curvatures under different loading conditions.Moreover,this formulation has been used to predict the effect of combined electric and magnetic loads on the mechanical response of panels with different curvatures and lamination schemes.As a consequence,this theory can be applied in engineering applications where the combined effect of electric and magnetic loads is crucial,thus facilitating their study and design.An existing limitation of this study is that the solution is that it is derived only for structures with uniform curvature,cross-ply lamination scheme,and simply supported boundary conditions.Furthermore,it requires that each lamina within the stacking sequence exhibits magneto-electro-elastic behavior.Therefore,at the present stage,it cannot be used for multifield analysis of classical composite structures with magneto-electric patches.A further enhancement of the research work could be the derivation of a solution employing a numerical technique,to overcome the limitations of the Navier method.In this way,the same theory may be adopted to predict the multifield response of structures with variable curvatures and thickness,as well as anisotropic materials and more complicated boundary conditions.Acknowledgement:The authors are grateful to the Department of Innovation Engineering of Univer-sity of Salento for the support.展开更多
This study presents a generalized two-dimensional model for evaluating the stationary hygro-thermo-mechanical response of laminated shell structures made of advanced materials.It introduces a generalized kinematic mod...This study presents a generalized two-dimensional model for evaluating the stationary hygro-thermo-mechanical response of laminated shell structures made of advanced materials.It introduces a generalized kinematic model,enabling the assessment of arbitrary values of temperature variation and mass concentration variation for the unvaried configuration at the top and bottom surfaces.This is achieved through the Equivalent Layer-Wise description of the unknown field variable using higher-order polynomials and zigzag functions.In addition,an elastic foundation is modeled utilizing the Winkler-Pasternak theory.The fundamental equations,derived from the total free energy of the system,are solved analytically using Navier’s method.Then,the Fourier-based generalized differential quadrature numerical method is adopted to efficiently recover the through-the-thickness distribution of secondary variables in agreement with the hygro-thermal loading conditions.The formulation is applied in some examples of investigation where the response of panels of different curvature and lamination schemes is evaluated under external hygro-thermal fluxes and prescribed values of temperature and moisture concentration.In addition,this study investigates the effect of the hygro-thermal coupling due to Dufour and Soret effect.The present formulation is verified to be a valuable tool for reducing computational effort and determining the effect on the mechanical response of laminated structures in a thermal and hygrometric environment.展开更多
The modeling of cross-ply composite laminates using numerical methods has been a difficult task,leading to the development of various finite element method and other analytical solutions.However,as materials science a...The modeling of cross-ply composite laminates using numerical methods has been a difficult task,leading to the development of various finite element method and other analytical solutions.However,as materials science advances,this problem has become more complex,presenting new challenges that require reliable and novel approaches.In this study,we propose the utilization of machine learning,specifically physics informed neural networks(PINN),for the first time to examine the behavior of composite plate.By solving a system of partial differential equations derived from the virtual work equilibrium principle,PINN are employed as a method to solve these equations using a generalized strong-form approach.To address the issue of imbalanced loss functions,we also propose adjusting the loss function in this research.Once trained,PINN serve as a surrogate model capable of predicting displacements and stresses in cross-ply composite laminates.To demonstrate the effectiveness and reliability of PINN,we investigate two examples of laminates with different material distributions and boundary conditions including boundary conditions on displacement and boundary conditions on stress,comparing the results with the benchmark Navier solution.The research and obtained results showcase the performance and accuracy of PINN,highlighting their potential as a surrogate model for solving problems related to cross-ply composite laminates.展开更多
In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate. Unlike any other theory, the number of unknown functions involve...In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Two common types of functionally graded sandwich plates, namely, the sandwich with fimctionally graded facesheet and homogeneous core and the sandwich with homogeneous facesheet and functionally graded core, are considered. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinu- soidal loading has been obtained by using the Navier method. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of functionally graded sandwich plates.展开更多
Bending analysis of functionally graded plates using the two variable refined plate theory is presented in this paper.The number of unknown functions involved is reduced to merely four,as against five in other shear d...Bending analysis of functionally graded plates using the two variable refined plate theory is presented in this paper.The number of unknown functions involved is reduced to merely four,as against five in other shear deformation theories. The variationally consistent theory presented here has, in many respects,strong similarity to the classical plate theory. It does not require shear correction factors,and gives rise to such transverse shear stress variation that the transverse shear stresses vary parabolically across the thickness and satisfy shear stress free surface conditions.Material properties of the plate are assumed to be graded in the thickness direction with their distributions following a simple power-law in terms of the volume fractions of the constituents.Governing equations are derived from the principle of virtual displacements, and a closed-form solution is found for a simply supported rectangular plate subjected to sinusoidal loading by using the Navier method.Numerical results obtained by the present theory are compared with available solutions,from which it can be concluded that the proposed theory is accurate and simple in analyzing the static bending behavior of functionally graded plates.展开更多
This paper uses the four-variable refined plate theory （RPT） for the free vibration analysis of functionally graded material （FGM） sandwich rectangular plates. Unlike other theories, there are only four unknown fu...This paper uses the four-variable refined plate theory （RPT） for the free vibration analysis of functionally graded material （FGM） sandwich rectangular plates. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton＇s principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-order theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.展开更多
In this paper,a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded plate.Unlike any other theory,the number of unknown functions involved is only fo...In this paper,a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded plate.Unlike any other theory,the number of unknown functions involved is only four,as against five in case of other shear deformation theories.The theory presented is variationally consistent,has strong similarity with classical plate theory inmany aspects,does not require shear correction factor,and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions.The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents.Numerical illustrations concerned flexural behavior of FG plates with Metal-Ceramic composition.Parametric studies are performed for varying ceramic volume fraction,volume fraction profiles,aspect ratios and length to thickness ratios.The validity of the present theory is investigated by comparing some of the present results with those of the classical,the first-order and the other higher-order theories.It can be concluded that the proposed theory is accurate and simple in solving the static behavior of functionally graded plates.展开更多
文摘This paper discusses the elastic equilibrium problems of anisotropic skew thin plate of variable thickness simply supported on all four sides in nonlinear theories, and uses the Navier method to seek an approach to the problem, and to illustrate the solution with the examples. In conclusion, the mention is made of the scope of application and the convergency of the solution.
基金funded by the Project PNRR M4C2—Innovation Grant DIRECT:Digital twIns foR EmergenCy supporT—CUP F83C22000740001.
文摘Recent engineering applications increasingly adopt smart materials,whose mechanical responses are sensitive to magnetic and electric fields.In this context,new and computationally efficient modeling strategies are essential to predict the multiphysic behavior of advanced structures accurately.Therefore,the manuscript presents a higher-order formulation for the static analysis of laminated anisotropic magneto-electro-elastic doubly-curved shell structures.The fundamental relations account for the full coupling between the electric field,magnetic field,and mechanical elasticity.The configuration variables are expanded along the thickness direction using a generalized formulation based on the Equivalent Layer-Wise approach.Higher-order polynomials are selected,allowing for the assessment of prescribed values of the configuration variables at the top and bottom sides of solids.In addition,an effective strategy is provided for modeling general surface distributions of mechanical pressures and electromagnetic external fluxes.The model is based on a continuum-based formulation which employs an analytical homogenization of the multifield material properties,based on Mori&Tanaka approach,of a magneto-electro-elastic composite material obtained from a piezoelectric and a piezomagnetic phase,with coupled magneto-electro-elastic effects.A semi-analytical Navier solution is applied to the fundamental equations,and an efficient post-processing equilibrium-based procedure is here used,based on the numerical assessment with the Generalized Differential Quadrature(GDQ)method,to recover the response of three-dimensional shells.The formulation is validated through various examples,investigating the multifield response of panels of different curvatures and lamination schemes.An efficient homogenization procedure,based on the Mori&Tanaka approach,is employed to obtain the three-dimensional constitutive relation of magneto-electro-elastic materials.Each model is validated against three-dimensional finite-element simulations,as developed in commercial codes.Furthermore,the full coupling effect between the electric and magnetic response is evaluated via a parametric investigation,with useful insights for design purposes of many engineering applications.The paper,thus,provides a formulation for the magneto-electro-elastic analysis of laminated structures,with a high computational efficiency,since it provides results with three-dimensional capabilities with a two-dimensional formulation.The adoption of higher-order theories,indeed,allows us to efficiently predict not only the mechanical response of the structure as happens in existing literature,but also the through-the-thickness distribution of electric and magnetic variables.A novel higher-order theory has been proposed in this work for the magneto-electro-elastic analysis of laminated shell structures with varying curvatures.This theory employs a generalized method to model the distribution of the displacement field components,electrostatic,and magneto-static potential,accounting for higher-order polynomials.The thickness functions have been defined to prescribe the arbitrary values of configuration variables at the top and bottom surfaces,even though the model is ESL-based.The fundamental governing equations have been derived in curvilinear principal coordinates,considering all coupling effects among different physical phenomena,including piezoelectric,piezomagnetic,and magneto-electric effects.A homogenization algorithm based on a Mori&Tanaka approach has been adopted to obtain the equivalent magneto-electro-mechanical properties of a two-phase transversely isotropic composite.In addition,an effective method has been adopted involving the external loads in terms of surface tractions,as well as the electric and magnetic fluxes.In the post-processing stage,a GDQ-based procedure provides the actual 3D response of a doubly-curved solid.The model has been validated through significant numerical examples,showing that the results of this semi-analytical theory align well with those obtained from 3D numerical models from commercial codes.In particular,the accuracy of the model has been verified for lamination schemes with soft layers and various curvatures under different loading conditions.Moreover,this formulation has been used to predict the effect of combined electric and magnetic loads on the mechanical response of panels with different curvatures and lamination schemes.As a consequence,this theory can be applied in engineering applications where the combined effect of electric and magnetic loads is crucial,thus facilitating their study and design.An existing limitation of this study is that the solution is that it is derived only for structures with uniform curvature,cross-ply lamination scheme,and simply supported boundary conditions.Furthermore,it requires that each lamina within the stacking sequence exhibits magneto-electro-elastic behavior.Therefore,at the present stage,it cannot be used for multifield analysis of classical composite structures with magneto-electric patches.A further enhancement of the research work could be the derivation of a solution employing a numerical technique,to overcome the limitations of the Navier method.In this way,the same theory may be adopted to predict the multifield response of structures with variable curvatures and thickness,as well as anisotropic materials and more complicated boundary conditions.Acknowledgement:The authors are grateful to the Department of Innovation Engineering of Univer-sity of Salento for the support.
基金funded by the Project PNRR M4C2—Innovation grant DIRECT:Digital twIns foR EmergenCy supporT—CUP F83C22000740001.
文摘This study presents a generalized two-dimensional model for evaluating the stationary hygro-thermo-mechanical response of laminated shell structures made of advanced materials.It introduces a generalized kinematic model,enabling the assessment of arbitrary values of temperature variation and mass concentration variation for the unvaried configuration at the top and bottom surfaces.This is achieved through the Equivalent Layer-Wise description of the unknown field variable using higher-order polynomials and zigzag functions.In addition,an elastic foundation is modeled utilizing the Winkler-Pasternak theory.The fundamental equations,derived from the total free energy of the system,are solved analytically using Navier’s method.Then,the Fourier-based generalized differential quadrature numerical method is adopted to efficiently recover the through-the-thickness distribution of secondary variables in agreement with the hygro-thermal loading conditions.The formulation is applied in some examples of investigation where the response of panels of different curvature and lamination schemes is evaluated under external hygro-thermal fluxes and prescribed values of temperature and moisture concentration.In addition,this study investigates the effect of the hygro-thermal coupling due to Dufour and Soret effect.The present formulation is verified to be a valuable tool for reducing computational effort and determining the effect on the mechanical response of laminated structures in a thermal and hygrometric environment.
基金the support from Ho Chi Minh City Open University under the Basic Research Fund(No.E2023.03.2).
文摘The modeling of cross-ply composite laminates using numerical methods has been a difficult task,leading to the development of various finite element method and other analytical solutions.However,as materials science advances,this problem has become more complex,presenting new challenges that require reliable and novel approaches.In this study,we propose the utilization of machine learning,specifically physics informed neural networks(PINN),for the first time to examine the behavior of composite plate.By solving a system of partial differential equations derived from the virtual work equilibrium principle,PINN are employed as a method to solve these equations using a generalized strong-form approach.To address the issue of imbalanced loss functions,we also propose adjusting the loss function in this research.Once trained,PINN serve as a surrogate model capable of predicting displacements and stresses in cross-ply composite laminates.To demonstrate the effectiveness and reliability of PINN,we investigate two examples of laminates with different material distributions and boundary conditions including boundary conditions on displacement and boundary conditions on stress,comparing the results with the benchmark Navier solution.The research and obtained results showcase the performance and accuracy of PINN,highlighting their potential as a surrogate model for solving problems related to cross-ply composite laminates.
文摘In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Two common types of functionally graded sandwich plates, namely, the sandwich with fimctionally graded facesheet and homogeneous core and the sandwich with homogeneous facesheet and functionally graded core, are considered. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinu- soidal loading has been obtained by using the Navier method. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending behavior of functionally graded sandwich plates.
文摘Bending analysis of functionally graded plates using the two variable refined plate theory is presented in this paper.The number of unknown functions involved is reduced to merely four,as against five in other shear deformation theories. The variationally consistent theory presented here has, in many respects,strong similarity to the classical plate theory. It does not require shear correction factors,and gives rise to such transverse shear stress variation that the transverse shear stresses vary parabolically across the thickness and satisfy shear stress free surface conditions.Material properties of the plate are assumed to be graded in the thickness direction with their distributions following a simple power-law in terms of the volume fractions of the constituents.Governing equations are derived from the principle of virtual displacements, and a closed-form solution is found for a simply supported rectangular plate subjected to sinusoidal loading by using the Navier method.Numerical results obtained by the present theory are compared with available solutions,from which it can be concluded that the proposed theory is accurate and simple in analyzing the static bending behavior of functionally graded plates.
文摘This paper uses the four-variable refined plate theory （RPT） for the free vibration analysis of functionally graded material （FGM） sandwich rectangular plates. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton＇s principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-order theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.
文摘In this paper,a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded plate.Unlike any other theory,the number of unknown functions involved is only four,as against five in case of other shear deformation theories.The theory presented is variationally consistent,has strong similarity with classical plate theory inmany aspects,does not require shear correction factor,and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions.The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents.Numerical illustrations concerned flexural behavior of FG plates with Metal-Ceramic composition.Parametric studies are performed for varying ceramic volume fraction,volume fraction profiles,aspect ratios and length to thickness ratios.The validity of the present theory is investigated by comparing some of the present results with those of the classical,the first-order and the other higher-order theories.It can be concluded that the proposed theory is accurate and simple in solving the static behavior of functionally graded plates.
