Sensitivity analyses are performed numerically from a mathematical model and the probability of failure is calculated by the First Order Reliability Method. Because of use of constant smoothing functions in the ES-FEM, only one Gaussian point is required for each smoothing domain ensuring that the total number of variables in the resulting optimization problem is kept to a minimum compared with standard finite element formulation. Numerical examples are presented to show the validity and effectiveness of the present method. The lower bound shakedown theorem for the determination of shakedown loading factors leads to nonlinear convex optimization problems.

For their solution, the use of interior-point methods has become common practice. In this paper, an extended formulation of the interior-point method for shakedown analysis is presented for von Mises-type materials. The formulation is generalized for the case of arbitrary finite numbers of loading cases. Numerical details of the algorithm are given and the described methodology is illustrated by a numerical example.

The strength as well as the ductility of a structure may be estimated by performing an elastoplastic analysis. In such an analysis structural loading is incrementally applied through a proportional loading factor in accordance to a predefined loading pattern. During this process we have continuous plasticizations of various parts of the structure. For a more accurate description of the physical process, possible deplasticizations should also be taken into account.

Thus a nonholonomic material behavior should be followed. In this work such an analysis is performed in an efficient way.

The basis of the approach is the formulation of the incremental problem as a convex parametric quadratic programming PQP problem between two successive plastic hinges. The solution of this problem is done by assuming a fictitious load factor which establishes a search direction for the next plasticization. The true load factor is established when the plastic hinge that is closest to open really opens.

An example of application, which serves as benchmark, is also included. This paper is concerned with the elastic plastic response of a two-bar system with temperature-dependent elastic coefficients under cyclic thermomechanical loadings.

### Direct Methods 2

Such materials are characterized by lack of results concerning the asymptotic behaviors and conditions for shakedown occurrence. This study shows that the considered simple structure is sufficiently complex to experience different periodic long term behaviors as in classical elastoplasticity.

The main result of this work is that the residual stress and strain fields are time-dependent even when shakedown occurs. Finally, numerical results performed by an incremental finite element procedure are presented. Conceived as an extended homogenization procedure, a multiphase approach for ascertaining the macroscopic behavior of reinforced soil structures has been developed in the last years.

This contribution is dedicated to the evaluation of the yield strength properties of soils reinforced by linear inclusions by making use of a homogenization procedure, in which the reinforced soil is regarded as a periodic composite, as a first calculation, and using the multiphase model. It appears from such a calculation that only the multiphase model is able to capture scale and boundary effects, which may play an important role in the yield design of reinforced structures. The behavior of soils reinforced by micropile networks is still not fully understood due to the lack of accurate modelling capabilities.

Particularly, the complex geometry of large soil-micropile systems makes accurate calculation of the bearing capacity of the reinforced soil a computational challenge. This complexity requires highly detailed and finely discretized models to achieve reasonable accuracy using direct numerical methods. Such models lead to large scale numerical optimization problems that are hardly tractable using a personal computer.

Recently a decomposition strategy with domain overlap has proved successful in solving very large kinematic and static limit analysis problems with limited computing resources. It consists of splitting the original problem into limit analysis subproblems that are smaller in size. The present paper reports enhancements made to the original decomposition method.

In particular, the method is made capable of solving the classical punch problem with Tresca or Coulomb soils.

## Limit State of Materials and Structures | woodcnilithibi.ml

This benchmark problem is considered as a limit case of a soil reinforced by micropiles. The paper then describes the application of the decomposition method to determine rigorous kinematic and static bounds to the bearing capacity of a soil reinforced by a micropile group according to a 2D plane strain model. For interface stresses obeying a von Mises criterion, we derive closed-form expressions of the parametric equations defining the yield surface.

World Scientific. Lahellec, N. On the effective behavior of nonlinear inelastic composites: I. Incremental variational principles. Journal of the Mechanics and Physics of Solids, 55 9 , Michel, J.

Effective properties of composite materials with periodic microstructure: a computational approach. Computer methods in applied mechanics and engineering, , Nonuniform transformation field analysis. International journal of solids and structures, 40 25 , Computational analysis of nonlinear composite structures using the nonuniform transformation field analysis.

Moulinec, H.

## SIAM Review

A numerical method for computing the overall response of nonlinear composites with complex microstructure. Intraphase strain heterogeneity in nonlinear composites: a computational approach. Pisano, A. A numerical approach for limit analysis of orthotropic composite laminates. International journal for numerical methods in engineering, 70 1 , Mechanically fastened joints in composite laminates: Evaluation of load bearing capacity. Composites Part B: Engineering, 42 4 , Peak load prediction of multi-pin joints FRP laminates by limit analysis. Composite Structures, 96, Ponter, A.

## Limit States of Materials and Structures

Limit state solutions, based upon linear elastic solutions with a spatially varying elastic modulus. Computer Methods in Applied Mechanics and Engineering, , Limit analysis for a general class of yield conditions. Qin, Q. Macro-micro theory on multi-field coupling behavior of heterogeneous materials. Ri, J. A modified algorithm of linear matching method for limit analysis.

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Archive of Applied Mechanics, 87 8 , Add Reviews.