Virtual element formulation for gradient elasticity
نویسندگان
چکیده
Abstract The virtual element method has been developed over the last decade and applied to problems in solid mechanics. Different formulations have used regarding order of ansatz, stabilization a wide range including elastic inelastic materials fracturing processes. This paper is concerned with elements for higher gradient theories solids using possibility, inherent methods, formulating C 1 -continuous ansatz functions simple efficient way.
منابع مشابه
A Stabilized Mixed Finite Element Method for Finite Elasticity Formulation for Linear Displacement and Pressure Interpolation
A stabilized mixed finite element method for finite elasticity is presented. The method circumvents the fulfillment of the Ladyzenskaya-Babuska-Brezzi condition by adding mesh-dependent terms, which are functions of the residuals of the Euler-Lagrange equations, to the usual Galerkin method. The weak form and the linearized weak form are presented in terms of the reference and current configura...
متن کاملA variational formulation with rigid-body constraints for finite elasticity: theory, finite element implementation, and applications
This paper presents a new variational principle in finite elastostatics applicable to arbitrary elastic solids that may contain constitutively rigid spatial domains (e.g., rigid inclusions). The basic idea consists in describing the constitutive rigid behavior of a given spatial domain as a set of kinematic constraints over the boundary of the domain. From a computational perspective, the propo...
متن کاملA New Mixed Formulation for Elasticity
In this paper we present a new mixed variational formulation for the problem of linear elastostatics. Our formulation is very similar to the classical HellingerReissner formulation, but appears superior for finite element discretization. To make plain the relation between the Hellinger-Reissner formulation and the present one, we consider first an elastic body occupying a region g? in Euclidean...
متن کاملNovel differential quadrature element method for higher order strain gradient elasticity theory
In this paper, we propose a novel and efficient differential quadrature element based on Lagrange interpolation to solve a sixth order partial differential equations encountered in non-classical beam theories. These non-classical theories render displacement, slope and curvature as degrees of freedom for an Euler-Bernoulli beam. A generalize scheme is presented herein to implementation the mult...
متن کاملBoundary Element Method for Elasticity Problems
Another general numerical method has recently emerged that provides good computational abilities and has some particular advantages when compared to FEM. The technique known as the boundary element method (BEM) has been widely used by computational mechanics investigators leading to the development of many private and commercial codes. Similar to the finite element method, BEM can analyze many ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Mechanica Sinica
سال: 2023
ISSN: ['1614-3116', '0567-7718']
DOI: https://doi.org/10.1007/s10409-022-22306-x