Abdelkader Hachemi

Numerical shakedown analysis of damaged structures

A numerical method is proposed to predict the failure of mechanical structures. It is based on the generalization of the classical static shakedown theorem to damaged inelastic structures. Ductile plastic damage is taken into account by using the models of Lemaitre and Shichun-Hua. The obtained results are compared in the special case of limit analysis to those obtained by incremental methods.

Shakedown and Optimization Analysis of Periodic Composites

In this work, non-conforming three-dimensional finite elements are used for the limit and shakedown analysis of periodic metal-matrix composites. The optimal design variables, such as fiber distribution and various volume fractions are investigated. Combined with homogenization theory, the global safe loading domains for the composites, as well as the global homogenized material parameters are determined, which opens the way for global structural design.

PROGRESS IN THE APPLICATION OF LOWER BOUND DIRECT METHODS IN STRUCTURAL DESIGN

Based on the lower-bound direct methods, namely limit and shakedown analysis, it is shown in this paper how these methods can be used in a constructive manner for structural industrial design. The proposed methods are based on finite element analyses and numerical optimization to determine the admissible loading. Numerical applications are presented and compared with existing results in literatures.

On Recent Progress in Shakedown Analysis and Applications to Large-Scale Problems

Shakedown and Limit Analysis have proven to be powerful tools to determine limit states of mechanical structures operating beyond the elastic limit under monotonous or variable thermo-mechanical loads. In this paper, recent results obtained by using the lower-bound theorem of shakedown analysis are presented focusing on new methods for solving large-scale problems by using a selective algorithm. Illustrative examples from mechanical and pavement engineering are presented.

Failure Investigation of Fiber-Reinforced Composite Materials by Shakedown Analysis

A methodology is proposed to investigate failure of composite materials under thermo-mechanical variable loads. By using the homogenization technique of periodic media, the plastically admissible ranges of macroscopic stresses can be found from the shakedown analysis of representative volume elements of the considered composite.

Progress in Plastic Design of Composites

In this paper, the lower-bound of direct methods is applied to fiber reinforced metal matrix periodic composites. Three boundary conditions for the localization problem are discussed and the influence of hardening matrix material is studied. Furthermore, in combination with homogenization theory, plastic material parameters are predicted by using yield loci fitting on the macroscopic limit stress domain. The proposed approach is validated through a numerical example of unidirectional periodic composites with square fiber patterns.

Plastic Design of Composites by Direct Methods

The paper discusses a method for direct evaluation of the yield values of fiber‐reinforced composites under variable loading. The optimal design variables, such as the fiber distribution and proper volume fraction for the composites under limit and shakedown conditions can be found by using Direct Methods.

Advanced Material Modelling in Shakedown Theory

The aim of this lecture is to present possibilities how to extend the validity of shakedown theory to other than linear elastic-ideal plastic or linear elastic- unlimited linear hardening material behaviour in conjunction with the validity of the normality rule. More precisely, the following items will be discussed: application of the General Standard Material Model, introduction of material damage in shakedown theory, use of no-associated flow rules and the notion of the Sanctuary of Elasticity.

Limit Loads for Structural Elements Made of Heterogeneous Materials

A numerical method is presented for determining the limit loads of periodically heterogeneous structures subjected to variable loads. The Melan’s lower-bound shakedown theorem was applied to representative volume elements. Combined with the homogenization technique, the homogenized material properties were determined through transformation from the mesoscopic to macroscopic admissible loading domains. For the numerical applications, solid non-conforming finite element discretization and large-scale nonlinear optimization, based on an interior-point-algorithm were used. The methodology is illustrated by the application to pipes models. This way, the proposed method provides a direct numerical approach to evaluate the macroscopic strength of heterogeneous structures with periodic micro- or meso-structure as a useful tool for the design of structures.© 2012 ASME

Recent Advances in Lower Bound Shakedown Analysis

The special interest in lower bound shakedown analysis is that it provides, at least in principle, safe operating conditions for sensitive structures or structural elements under fluctuating thermo-mechanical loading as to be found in power- and process engineering. In this paper achievements obtained over the last years to introduce more sophisticated material models into the framework of shakedown analysis are developed. Also new algorithms will be presented that allow using the addressed numerical methods as post-processor for commercial finite element codes. Examples from practical engineering will illustrate the potential of the methodology.Copyright