Multigrid finite-element solvers using the corotational formulation of finite elements provide an attractive means for the simulation of deformable bodies exhibiting linear elastic response. The separation of rigid body motions from the total element motions using purely geometric methods or polar decomposition of the deformation gradient, however, can introduce instabilities for large element ...

This paper sheds more light on the co-rotational element formulation for beams with uniform cross-section. The co-rotational elements are commonly used in problems in which a structure undergoes a large deformation. In this study, the foregoing element obeys the Euler-Bernoulli beam assumptions. Unlike the formulations presented in the literature, in this paper, a number of local nodal coordina...

The primary objectives of the present exposition focus on the applicability of corotational stress rate hypoelasticity models and the design leading to new stress update formulations for subsequent applications. In this regard, various corotational stress rate hypoelasticity models are "rst studied. The conclusion that only the logarithmic stress rate hypoelasticity is suitable for "nite deform...

Various corotational schemes for solid, shell, bending plate and beam elements have been proposed so far. Nevertheless, this approach has rarely been utilized for membrane problems. In this paper, a new quadrilateral element will be suggested for solving nonlinear membranes. The simplicity, rapid convergence and high accuracy of the formulation are the three main characteristics of the presente...

A numerical investigation is carried out in this work in order to evaluate the computational performance of a numerical model based on isogeometric analysis for applications on geometrically nonlinear elastodynamics. In the FEM (finite element method) practice, it is well known that the Newmark’s method is unconditionally stable for linear structural systems, but this characteristic is frequent...

In this paper, we present a multigrid framework for constructing implicit, yet interactive solvers for the governing equations of motion of deformable volumetric bodies. We have integrated linearized, corotational linearized and non-linear Green strain into this framework. Based on a 3D finite element hierarchy, this approach enables realistic simulation of objects exhibiting an elastic modulus...