In the presentmanuscript,a Layer-Wise(LW)generalizedmodel is proposed for the linear static analysis of doublycurved shells constrained with general boundary conditions under the influence of concentrated and surface ...In the presentmanuscript,a Layer-Wise(LW)generalizedmodel is proposed for the linear static analysis of doublycurved shells constrained with general boundary conditions under the influence of concentrated and surface loads.The unknown field variable is modelled employing polynomials of various orders,each of them defined within each layer of the structure.As a particular case of the LW model,an Equivalent Single Layer(ESL)formulation is derived too.Different approaches are outlined for the assessment of external forces,as well as for non-conventional constraints.The doubly-curved shell is composed by superimposed generally anisotropic laminae,each of them characterized by an arbitrary orientation.The fundamental governing equations are derived starting from an orthogonal set of principal coordinates.Furthermore,generalized blending functions account for the distortion of the physical domain.The implementation of the fundamental governing equations is performed bymeans of the Generalized Differential Quadrature(GDQ)method,whereas the numerical integrations are computed employing theGeneralized IntegralQuadrature(GIQ)method.In the post-processing phase,an effective procedure is adopted for the reconstruction of stress and strain through-the-thickness distributions based on the exact fulfillment of three-dimensional equilibrium equations.A series of systematic investigations are performed in which the static response of structures with various curvatures and lamination schemes,calculated by the present methodology,have been successfully compared to those ones obtained fromrefined finite element three-dimensional simulations.Even though the present LW approach accounts for a two-dimensional assessment of the structural problem,it is capable of well predicting the three-dimensional response of structures with different characteristics,taking into account a reduced computational cost and pretending to be a valid alternative to widespread numerical implementations.展开更多
Similar to the very vast prior literature on analyzing laminated composite structures,“higher-order”and“layer-wise higher-order”plate and shell theories for functionally-graded(FG)materials and structures are also...Similar to the very vast prior literature on analyzing laminated composite structures,“higher-order”and“layer-wise higher-order”plate and shell theories for functionally-graded(FG)materials and structures are also widely popularized in the literature of the past two decades.However,such higher-order theories involve(1)postulating very complex assumptions for plate/shell kinematics in the thickness direction,(2)defining generalized variables of displacements,strains,and stresses,and(3)developing very complex governing equilibrium,compatibility,and constitutive equations in terms of newly-defined generalized kinematic and generalized kinetic variables.Their industrial applications are thus hindered by their inherent complexity,and the fact that it is difficult for end-users(front-line structural engineers)to completely understand all the newly-defined generalized DOFs for FEM in the higher-order and layer-wise theories.In an entirely different way,very simple 20-node and 27-node 3-D continuum solid-shell elements are developed in this paper,based on the simple theory of 3D solid mechanics,for static and dynamic analyses of functionally-graded plates and shells.A simple Over-Integration(a 4-point Gauss integration in the thickness direction)is used to evaluate the stiffness matrices of each element,while only a single element is used in the thickness direction without increasing the number of degrees of freedom.A stress-recovery approach is used to compute the distribution of transverse stresses by considering the equations of 3D elasticity in Cartesian as well as cylindrical polar coordinates.Comprehensive numerical results are presented for static and dynamic analyses of FG plates and shells,which agree well,either with the existing solutions in the published literature,or with the computationally very expensive solutions obtained by using simple 3D isoparametric elements(with standard Gauss Quadrature)available in NASTRAN(wherein many 3D elements are used in the thickness direction to capture the varying material properties).The effects of the material gradient index,the span-to-thickness ratio,the aspect ratio and the boundary conditions are also studied in the solutions of FG structures.Because the proposed methodology merely involves:(2)standard displacement DOFs at each node,(2)involves a simple 4-point Gaussian over-integration in the thickness direction,(3)relies only on the simple theory of solid mechanics,and(4)is capable of accurately and efficiently predicting the static and dynamical behavior of FG structures in a very simple and cost-effective manner,it is thus believed by the authors that the painstaking and cumbersome development of“higher-order”or“layer-wise higher-order”theories is not entirely necessary for the analyses of FG plates and shells.展开更多
The present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic.The refined models u...The present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic.The refined models used are derived from Carrera’s Unified Formulation(CUF)and they permit the vibration modes along the thickness to be accurately described.The finite-element method is employed and the plate element implemented has nine nodes,and the mixed interpolation of tensorial component(MITC)method is used to contrast the membrane and shear locking phenomenon.The related governing equations are derived from the principle of virtual displacement,extended to the analysis of electromechanical problems.An isotropic plate with piezoelectric patches is analyzed,with clamped-free boundary conditions and subjected to open-and short-circuit configurations.The results,obtained with different theories,are compared with the higher-order type solutions given in the literature.The conclusion is reached that the plate element based on the CUF is more suitable and efficient compared to the classical models in the study of multilayered structures embedding piezo-patches.展开更多
文摘In the presentmanuscript,a Layer-Wise(LW)generalizedmodel is proposed for the linear static analysis of doublycurved shells constrained with general boundary conditions under the influence of concentrated and surface loads.The unknown field variable is modelled employing polynomials of various orders,each of them defined within each layer of the structure.As a particular case of the LW model,an Equivalent Single Layer(ESL)formulation is derived too.Different approaches are outlined for the assessment of external forces,as well as for non-conventional constraints.The doubly-curved shell is composed by superimposed generally anisotropic laminae,each of them characterized by an arbitrary orientation.The fundamental governing equations are derived starting from an orthogonal set of principal coordinates.Furthermore,generalized blending functions account for the distortion of the physical domain.The implementation of the fundamental governing equations is performed bymeans of the Generalized Differential Quadrature(GDQ)method,whereas the numerical integrations are computed employing theGeneralized IntegralQuadrature(GIQ)method.In the post-processing phase,an effective procedure is adopted for the reconstruction of stress and strain through-the-thickness distributions based on the exact fulfillment of three-dimensional equilibrium equations.A series of systematic investigations are performed in which the static response of structures with various curvatures and lamination schemes,calculated by the present methodology,have been successfully compared to those ones obtained fromrefined finite element three-dimensional simulations.Even though the present LW approach accounts for a two-dimensional assessment of the structural problem,it is capable of well predicting the three-dimensional response of structures with different characteristics,taking into account a reduced computational cost and pretending to be a valid alternative to widespread numerical implementations.
基金This research is supported by the Mechanics Section,Vehicle Technology Division,of the US Army Research Labs.The support of National Natural Science Foundation of China(grant No.11502069)Natural Science Foundation of Jiangsu Province(grant No.BK20140838)is also thankfully acknowledged.
文摘Similar to the very vast prior literature on analyzing laminated composite structures,“higher-order”and“layer-wise higher-order”plate and shell theories for functionally-graded(FG)materials and structures are also widely popularized in the literature of the past two decades.However,such higher-order theories involve(1)postulating very complex assumptions for plate/shell kinematics in the thickness direction,(2)defining generalized variables of displacements,strains,and stresses,and(3)developing very complex governing equilibrium,compatibility,and constitutive equations in terms of newly-defined generalized kinematic and generalized kinetic variables.Their industrial applications are thus hindered by their inherent complexity,and the fact that it is difficult for end-users(front-line structural engineers)to completely understand all the newly-defined generalized DOFs for FEM in the higher-order and layer-wise theories.In an entirely different way,very simple 20-node and 27-node 3-D continuum solid-shell elements are developed in this paper,based on the simple theory of 3D solid mechanics,for static and dynamic analyses of functionally-graded plates and shells.A simple Over-Integration(a 4-point Gauss integration in the thickness direction)is used to evaluate the stiffness matrices of each element,while only a single element is used in the thickness direction without increasing the number of degrees of freedom.A stress-recovery approach is used to compute the distribution of transverse stresses by considering the equations of 3D elasticity in Cartesian as well as cylindrical polar coordinates.Comprehensive numerical results are presented for static and dynamic analyses of FG plates and shells,which agree well,either with the existing solutions in the published literature,or with the computationally very expensive solutions obtained by using simple 3D isoparametric elements(with standard Gauss Quadrature)available in NASTRAN(wherein many 3D elements are used in the thickness direction to capture the varying material properties).The effects of the material gradient index,the span-to-thickness ratio,the aspect ratio and the boundary conditions are also studied in the solutions of FG structures.Because the proposed methodology merely involves:(2)standard displacement DOFs at each node,(2)involves a simple 4-point Gaussian over-integration in the thickness direction,(3)relies only on the simple theory of solid mechanics,and(4)is capable of accurately and efficiently predicting the static and dynamical behavior of FG structures in a very simple and cost-effective manner,it is thus believed by the authors that the painstaking and cumbersome development of“higher-order”or“layer-wise higher-order”theories is not entirely necessary for the analyses of FG plates and shells.
文摘The present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic.The refined models used are derived from Carrera’s Unified Formulation(CUF)and they permit the vibration modes along the thickness to be accurately described.The finite-element method is employed and the plate element implemented has nine nodes,and the mixed interpolation of tensorial component(MITC)method is used to contrast the membrane and shear locking phenomenon.The related governing equations are derived from the principle of virtual displacement,extended to the analysis of electromechanical problems.An isotropic plate with piezoelectric patches is analyzed,with clamped-free boundary conditions and subjected to open-and short-circuit configurations.The results,obtained with different theories,are compared with the higher-order type solutions given in the literature.The conclusion is reached that the plate element based on the CUF is more suitable and efficient compared to the classical models in the study of multilayered structures embedding piezo-patches.
