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 work presents a theoretical study for thermo-mechanical buckling of size-dependent magneto-electro-thermo-elastic func-tionally graded(METE-FG)nanoplates in thermal environments based on a refined trigonometric p...This work presents a theoretical study for thermo-mechanical buckling of size-dependent magneto-electro-thermo-elastic func-tionally graded(METE-FG)nanoplates in thermal environments based on a refined trigonometric plate theory.Temperature field has uniform,linear,and nonlinear distributions across the thick-ness.Nonlinear thermal loadings are considered as heat conduc-tion(HC)and sinusoidal temperature rise(STR).A power law function is applied to govern the gradation of material properties through the nanoplate thickness.Considering coupling impacts between magneto,electro,thermo-mechanical loadings,the equa-tions of motion,and distribution of magneto-electrical field across the thickness direction of the METE-FG nanoplate are derived.The exact solutions for critical buckling temperatures of METE-FG nanoplates are introduced implementing Navier’s method.Moreover,the accuracy of the present formulation is examined by comparing the obtained results with published ones.Furthermore,the effects played by the magneto-electrical field,various temperature rises,nonlocality,power law index,side-to-thickness ratio,and aspect ratio on the critical buckling tempera-ture response are all investigated and reported.展开更多
This research presents a finite element formulation based on four-variable refined plate theory for bending analysis of cross-ply and angle-ply laminated composite plates integrated with a piezoelectric fiber-reinforc...This research presents a finite element formulation based on four-variable refined plate theory for bending analysis of cross-ply and angle-ply laminated composite plates integrated with a piezoelectric fiber-reinforced composite actuator under electromechanical loading. The four-variable refined plate theory is a simple and efficient higher-order shear deformation theory, which predicts parabolic variation of transverse shear stresses across the plate thickness and satisfies zero traction conditions on the plate free surfaces. The weak form of governing equations is derived using the principle of minimum potential energy, and a 4-node non-conforming rectangular plate element with 8 degrees of freedom per node is introduced for discretizing the domain. Several benchmark problems are solved by the developed MATLAB code and the obtained results are compared with those from exact and other numerical solutions, showing good agreement.展开更多
This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate ...This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate change in both the thickness and length directions via power-law distributions and Mori-Tanaka model. The governing equation of motion of BDFG plate in the fluid-plate system is formulated basing on Hamilton's principle and the refined quasi three-dimensional (3D) plate theory with improved function f(z). The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to determine the added mass. The discrete system of equations is derived from the Galerkin weak form and numerically analyzed by IGA. The accuracy and reliability of the proposed solutions are verified by comparing the obtained results with those published in the literature. Moreover, the effects of the various parameters such as the interaction boundary condition, geometric parameter, submerged depth of plate, fluid density, fluid level, and the material volume control coefficients on the free vibration behavior of BDFG plate in the fluid medium are investigated in detail. Some major findings regarding the numerical results are withdrawn in conclusions.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
In this study,a finite element formulation based on the four-variable refined plate theory(RPT)is presented for forced vibration analysis of laminated viscoelastic composite plates integrated with a piezoelectric laye...In this study,a finite element formulation based on the four-variable refined plate theory(RPT)is presented for forced vibration analysis of laminated viscoelastic composite plates integrated with a piezoelectric layer.To the best of the authors’knowledge,this is the first time that the proposed approach is extended for study of the dynamic behavior of the smart viscoelastic plate.The utilized RPT which works for both thick and thin plates predicts a parabolic variation for transverse shear stresses across the plate thickness.Considering a linear viscoelastic model for the substrate material,the relaxation module is predicted by the Prony series.Using Hamilton’s principle,the weak form equation is constructed and a four-node rectangular plate element is utilized for discretizing the domain.The Newmark scheme is employed for advancing the solution in time.A MATLAB code is developed based on the formulations and several benchmark problems are solved.Comparing the findings with existing results in previous studies confirms the accuracy and efficiency of the proposed method.The dynamic response of the smart viscoelastic plates under various electromechanical loads is investigated and the results show that the.vibration can be passively controlled by adding and actuating the piezoelectric layer.The damping effects of viscoelastic parameters on the results are investigated,too.展开更多
This article presents a type of plate Finite Element(FE)models with adaptive mathematical refinement capabilities for modeling laminated smart structures with piezoelectric layers or distributed patches.The p-version ...This article presents a type of plate Finite Element(FE)models with adaptive mathematical refinement capabilities for modeling laminated smart structures with piezoelectric layers or distributed patches.The p-version shape functions are used in combination with the higher-order Layer-Wise(LW)kinematics adopting hierarchical Legendre polynomials.Node-Dependent Kinematics(NDK)is employed to implement local LW models in the regions with piezoelectric components and simulate the global substrate structure with the Equivalent Single-Layer(ESL)approach.Through the proposed NDK FE models,the electro-mechanical behavior of smart structures can be predicted with high fidelity and numerical efficiency,and various patch configurations can be conveniently modeled through one set of mesh grids.Moreover,the effectiveness and efficiency of the NDK FE approach are assessed through numerical examples and its application is demonstrated.展开更多
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 work presents a theoretical study for thermo-mechanical buckling of size-dependent magneto-electro-thermo-elastic func-tionally graded(METE-FG)nanoplates in thermal environments based on a refined trigonometric plate theory.Temperature field has uniform,linear,and nonlinear distributions across the thick-ness.Nonlinear thermal loadings are considered as heat conduc-tion(HC)and sinusoidal temperature rise(STR).A power law function is applied to govern the gradation of material properties through the nanoplate thickness.Considering coupling impacts between magneto,electro,thermo-mechanical loadings,the equa-tions of motion,and distribution of magneto-electrical field across the thickness direction of the METE-FG nanoplate are derived.The exact solutions for critical buckling temperatures of METE-FG nanoplates are introduced implementing Navier’s method.Moreover,the accuracy of the present formulation is examined by comparing the obtained results with published ones.Furthermore,the effects played by the magneto-electrical field,various temperature rises,nonlocality,power law index,side-to-thickness ratio,and aspect ratio on the critical buckling tempera-ture response are all investigated and reported.
文摘This research presents a finite element formulation based on four-variable refined plate theory for bending analysis of cross-ply and angle-ply laminated composite plates integrated with a piezoelectric fiber-reinforced composite actuator under electromechanical loading. The four-variable refined plate theory is a simple and efficient higher-order shear deformation theory, which predicts parabolic variation of transverse shear stresses across the plate thickness and satisfies zero traction conditions on the plate free surfaces. The weak form of governing equations is derived using the principle of minimum potential energy, and a 4-node non-conforming rectangular plate element with 8 degrees of freedom per node is introduced for discretizing the domain. Several benchmark problems are solved by the developed MATLAB code and the obtained results are compared with those from exact and other numerical solutions, showing good agreement.
基金This research is funded by Vietnam National Foundation for Science and Technology Development(NAFOSTED)under Grant number 107.02-2019.330.
文摘This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate change in both the thickness and length directions via power-law distributions and Mori-Tanaka model. The governing equation of motion of BDFG plate in the fluid-plate system is formulated basing on Hamilton's principle and the refined quasi three-dimensional (3D) plate theory with improved function f(z). The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to determine the added mass. The discrete system of equations is derived from the Galerkin weak form and numerically analyzed by IGA. The accuracy and reliability of the proposed solutions are verified by comparing the obtained results with those published in the literature. Moreover, the effects of the various parameters such as the interaction boundary condition, geometric parameter, submerged depth of plate, fluid density, fluid level, and the material volume control coefficients on the free vibration behavior of BDFG plate in the fluid medium are investigated in detail. Some major findings regarding the numerical results are withdrawn in conclusions.
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In this study,a finite element formulation based on the four-variable refined plate theory(RPT)is presented for forced vibration analysis of laminated viscoelastic composite plates integrated with a piezoelectric layer.To the best of the authors’knowledge,this is the first time that the proposed approach is extended for study of the dynamic behavior of the smart viscoelastic plate.The utilized RPT which works for both thick and thin plates predicts a parabolic variation for transverse shear stresses across the plate thickness.Considering a linear viscoelastic model for the substrate material,the relaxation module is predicted by the Prony series.Using Hamilton’s principle,the weak form equation is constructed and a four-node rectangular plate element is utilized for discretizing the domain.The Newmark scheme is employed for advancing the solution in time.A MATLAB code is developed based on the formulations and several benchmark problems are solved.Comparing the findings with existing results in previous studies confirms the accuracy and efficiency of the proposed method.The dynamic response of the smart viscoelastic plates under various electromechanical loads is investigated and the results show that the.vibration can be passively controlled by adding and actuating the piezoelectric layer.The damping effects of viscoelastic parameters on the results are investigated,too.
基金carried out within the project FULLCOMP(Fully analysis,design,manufacturing,and health monitoring of Composite structures),funded by the European Union Horizon 2020 Research and Innovation Program under the Marie Sklodowska Curie Grant Agreement(No.642121)the Russian Science Foundation(No.18-19-00092)the financial support from National Natural Science Foundation of China(No.52005451)。
文摘This article presents a type of plate Finite Element(FE)models with adaptive mathematical refinement capabilities for modeling laminated smart structures with piezoelectric layers or distributed patches.The p-version shape functions are used in combination with the higher-order Layer-Wise(LW)kinematics adopting hierarchical Legendre polynomials.Node-Dependent Kinematics(NDK)is employed to implement local LW models in the regions with piezoelectric components and simulate the global substrate structure with the Equivalent Single-Layer(ESL)approach.Through the proposed NDK FE models,the electro-mechanical behavior of smart structures can be predicted with high fidelity and numerical efficiency,and various patch configurations can be conveniently modeled through one set of mesh grids.Moreover,the effectiveness and efficiency of the NDK FE approach are assessed through numerical examples and its application is demonstrated.