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 article proposes an Equivalent Single Layer(ESL)formulation for the linear static analysis of arbitrarily-shaped shell structures subjected to general surface loads and boundary conditions.A parametrization of the...The article proposes an Equivalent Single Layer(ESL)formulation for the linear static analysis of arbitrarily-shaped shell structures subjected to general surface loads and boundary conditions.A parametrization of the physical domain is provided by employing a set of curvilinear principal coordinates.The generalized blendingmethodology accounts for a distortion of the structure so that disparate geometries can be considered.Each layer of the stacking sequence has an arbitrary orientation and is modelled as a generally anisotropic continuum.In addition,re-entrant auxetic three-dimensional honeycomb cells with soft-core behaviour are considered in the model.The unknown variables are described employing a generalized displacement field and pre-determined through-the-thickness functions assessed in a unified formulation.Then,a weak assessment of the structural problem accounts for shape functions defined with an isogeometric approach starting fromthe computational grid.Ageneralizedmethodology has been proposed to define two-dimensional distributions of static surface loads.In the same way,boundary conditions with three-dimensional features are implemented along the shell edges employing linear springs.The fundamental relations are obtained from the stationary configuration of the total potential energy,and they are numerically tackled by employing the Generalized Differential Quadrature(GDQ)method,accounting for nonuniform computational grids.In the post-processing stage,an equilibrium-based recovery procedure allows the determination of the three-dimensional dispersion of the kinematic and static quantities.Some case studies have been presented,and a successful benchmark of different structural responses has been performed with respect to various refined theories.展开更多
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
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.
文摘The article proposes an Equivalent Single Layer(ESL)formulation for the linear static analysis of arbitrarily-shaped shell structures subjected to general surface loads and boundary conditions.A parametrization of the physical domain is provided by employing a set of curvilinear principal coordinates.The generalized blendingmethodology accounts for a distortion of the structure so that disparate geometries can be considered.Each layer of the stacking sequence has an arbitrary orientation and is modelled as a generally anisotropic continuum.In addition,re-entrant auxetic three-dimensional honeycomb cells with soft-core behaviour are considered in the model.The unknown variables are described employing a generalized displacement field and pre-determined through-the-thickness functions assessed in a unified formulation.Then,a weak assessment of the structural problem accounts for shape functions defined with an isogeometric approach starting fromthe computational grid.Ageneralizedmethodology has been proposed to define two-dimensional distributions of static surface loads.In the same way,boundary conditions with three-dimensional features are implemented along the shell edges employing linear springs.The fundamental relations are obtained from the stationary configuration of the total potential energy,and they are numerically tackled by employing the Generalized Differential Quadrature(GDQ)method,accounting for nonuniform computational grids.In the post-processing stage,an equilibrium-based recovery procedure allows the determination of the three-dimensional dispersion of the kinematic and static quantities.Some case studies have been presented,and a successful benchmark of different structural responses has been performed with respect to various refined theories.
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.
