In the conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local different...In the conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature （LDQ） method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in the new approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directly approximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature is still kept. Numerical examples are provided to validate the LDQ method.展开更多
Rubber-like materials that are commonly used in structural applications are modelled using hyperelastic material models.Most of the hyperelastic materials are nearly incompressible,which poses challenges,i.e.,volumetr...Rubber-like materials that are commonly used in structural applications are modelled using hyperelastic material models.Most of the hyperelastic materials are nearly incompressible,which poses challenges,i.e.,volumetric locking during numerical modelling.There exist many formulations in the context of the finite element method,among which the mixed displacementpressure formulation is robust.However,such a displacement-pressure formulation is less explored in meshfree methods,which mitigates the problem associated with mesh distortion during large deformation.This work addresses this issue of alleviating volumetric locking in the element-free Galerkin method(EFGM),which is one of the popular meshfree methods.A two-field mixed variational formulation using the perturbed Lagrangian approach within the EFGM framework is proposed for modelling nearly incompressible hyperelastic material models,such as Neo-Hookean and Mooney-Rivlin.Taking advantage of the meshless nature of the EFGM,this work introduces a unique approach by randomly distributing pressure nodes across the geometry,following specific guidelines.A wide spectrum of problems involving bending,tension,compression,and contact is solved using two approaches of the proposed displacement-pressure node formulation involving regular and irregular pressure node distribution.It is observed that both approaches give accurate results compared to the reference results,though the latter offers flexibility in the pressure nodal distribution.展开更多
文摘In the conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature （LDQ） method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in the new approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directly approximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature is still kept. Numerical examples are provided to validate the LDQ method.
基金supported by the DST-SERB and VSSC,ISRO of the project titled“Functionality Enhancement through Design and Development of Advanced Finite Element Algorithms for STR tools”under IMPRINT.IIC(IMP/2019/000276)scheme.
文摘Rubber-like materials that are commonly used in structural applications are modelled using hyperelastic material models.Most of the hyperelastic materials are nearly incompressible,which poses challenges,i.e.,volumetric locking during numerical modelling.There exist many formulations in the context of the finite element method,among which the mixed displacementpressure formulation is robust.However,such a displacement-pressure formulation is less explored in meshfree methods,which mitigates the problem associated with mesh distortion during large deformation.This work addresses this issue of alleviating volumetric locking in the element-free Galerkin method(EFGM),which is one of the popular meshfree methods.A two-field mixed variational formulation using the perturbed Lagrangian approach within the EFGM framework is proposed for modelling nearly incompressible hyperelastic material models,such as Neo-Hookean and Mooney-Rivlin.Taking advantage of the meshless nature of the EFGM,this work introduces a unique approach by randomly distributing pressure nodes across the geometry,following specific guidelines.A wide spectrum of problems involving bending,tension,compression,and contact is solved using two approaches of the proposed displacement-pressure node formulation involving regular and irregular pressure node distribution.It is observed that both approaches give accurate results compared to the reference results,though the latter offers flexibility in the pressure nodal distribution.
