Nonlinear Deformation and Numerical Post-Buckling Analysis of Plate Structures Using the Assumed Natural Strain Concept

In this study, an efficient triangular element for the fast nonlinear analysis of moderately thick Mindlin–Reissner plates is proposed. The element is formulated using a newly developed method, which is based on the assumed natural strain concept, and called Continuously Variable Strain (CVS). The continuous higher-order strain field is proposed by using the fundamental lemma of the variational calculus. Furthermore, the updated Lagrangian tensor together with rigid body terms is employed allowing for large deformations. The proposed element (CVST10), which is obtained by minimizing the total potential energy, has only 10 degrees of freedom and demonstrates high-efficiency and fast convergence rate in analysis of problems with coarse and distorted meshes. The arc-length iterative technique is applied to handle the geometrically post-buckling behavior of homogeneous plates under various load and boundary conditions. Various numerical examples prove the accuracy of the proposed element.

Extension of the unsymmetric 8-node hexahedral solid element US-ATFH8 to geometrically nonlinear analysis

Purpose The purpose of this paper is to extend a recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with high distortion tolerance, which uses the analytical solutions of linear elasticity governing equations as the trial functions (analytical trial function) to geometrically nonlinear analysis. Design/methodology/approach Based on the assumption that these analytical trial functions can still properly work in each increment step during the nonlinear analysis, the present work concentrates on the construction of incremental nonlinear formulations of the unsymmetric element US-ATFH8 through two different ways: the general updated Lagrangian (UL) approach and the incremental co-rotational (CR) approach. The key innovation is how to update the stresses containing the linear analytical trial functions. Findings Several numerical examples for 3D structures show that both resulting nonlinear elements, US-ATFH8-UL and US-ATFH8-CR, perform very well, no matter whether regular or distorted coarse mesh is used, and exhibit much better performances than those conventional symmetric nonlinear solid elements. Originality/value The success of the extension of element US-ATFH8 to geometrically nonlinear analysis again shows the merits of the unsymmetric finite element method with analytical trial functions, although these functions are the analytical solutions of linear elasticity governing equations.

On the Contribution of Grain Boundary Sliding to Firn Densification – an Assessment using an Optimisation Approach

Physics based simulation approaches to firn densification often rely on the assumption that grain boundary sliding,first introduced by Alley (1987) to firn, is the leading process driving the first stage of densification. However, often so calledsemi empirical models are favored against the description of grain boundary sliding due to simplicity and uncertainties regard-ing model parameters. In this study, we are assessing the applicability of grain boundary sliding to firn using a numeric firn5densification model and an optimisation approach, for which we formulate variants of the constitutive relation by Alley (1987).The efficient model implementation based on an updated Lagrangian numerical scheme enables us to perform a large numberof simulations testing different model parameters, to find simulation results suiting 159 firn density profiles from Greenlandand Antarctica best. For most of the investigated locations a good agreement of simulated and measured firn density profileswas found. This implies that the constitutive relation by Alley (1987) characterises the fist stage of firn densification well, if10suitable model parameter are used. An analysis of the parameters that lead to best matches reveals a dependency on the meansurface mass balance. This may indicate an insufficient description of the load situation, as horizontal components of the stresstensor are usually neglected in one dimensional models of the firn column.