In this paper, a generalized particle system (GPS) method, a general method to describe multiple strong form representation based particle methods is described. Gradient, divergence, and Laplacian operators used in various strong form based particle method such as moving particle semi-implicit (MPS) method, smooth particle hydrodynamics (SPH), and peridynamics, can be described by the GPS metho...

A discontinuous Galerkin formulation of the Boundary Value Problem of finite-deformation elasticity is presented. The method is based on a general Hu-Washizu-de Veubeke functional allowing for displacement and stress discontinuities in the domain interior. It is shown that this approach naturally leads to the formulation of average stress fluxes at interelement boundaries in a finite element im...

This paper is concerned with the development of Trefftz p-element for twodimentional piezoelectric materials. Solutions in Stroh formalism for transversely isotropic piezoelectric materials are used for the intra-element displacement and electric potential (DEP) fields together with an independent DEP frame function field along element boundaries. The formulation is based on a modified variatio...

In this work shall be presented a stabilized finite element method to deal with incompressibility in solid mechanics. A mixed formulation involving pressure and displacement fields is used and a continuous linear interpolation is considered for both fields. To overcome the Ladyzhenskaya-Babuška-Brezzi condition, a stabilization technique based on the orthogonal sub-grid scale method is introduc...

A higher order displacement based formulation has been developed to investigate the plane strain edge vibrations or end modes in composite laminated sandwich plates. The formulation has been applied as an illustration, to the laminated sandwich plates made up of transversely isotropic laminae with the axes of symmetry lying in the plane of the lamina and core in-between. The results for isotrop...

In the present article two-dimensional hybrid equilibrium element formulation is initially developed, with quadratic, cubic, and quartic stress fields, for static analysis of compressible quasi-incompressible elastic solids in variational framework minimum complementary energy principle. Thereafter, high-order developed dynamic Toupin principle, which form Hamilton The Newmark time integration ...

This paper deals with a finite element method to solve interior fluid-structure vibration problems valid for compressible and incompressible fluids. It is based on a displacement formulation for both the fluid and the solid. The pressure of the fluid is also used as a variable for the theoretical analysis yielding a well posed mixed linear eigenvalue problem. Lowest order triangular Raviart-Tho...

This paper presents a C discontinuous Galerkin formulation for the simulation of thin shells. The method is based on Koiter’s shell model and allows finite element solutions to be obtained by using standard C Lagrange basis functions in terms of the displacement only. It invokes a curvature-like term by applying a lifting operation which transforms jumps in the normal rotation across element bo...

This article presents a finite element reduced order model for the nonlinear vibrations of piezoelectric layered beams with application to NEMS. In this model, the geometrical nonlinearities are taken into account through a von Kármán nonlinear strain–displacement relationship. The originality of the finite element electromechanical formulation is that the system electrical state is fully descr...