Limit Analysis of Strain Softening Frames Allowing for Geometric Nonlinearity

This paper extends classical limit analysis to account for strain softening and 2nd-order geometric nonlinearity simultaneously. The formulation is an instance of the challenging class of socalled (nonconvex) mathematical programs with equilibrium constraints (MPECs). A penalty algorithm is proposed to solve the MPEC. A practical frame example is provided to illustrate the approach

Iterative limit analysis of structures within a scaled boundary finite element framework

This paper presents an iterative elastic analysis approach to determine the collapse load limit of structures. The proposed scheme is based on the use of a modified elastic compensation method, where the structure is modeled within a scaled boundary finite element framework. The formulation takes the general form of polygon scaled boundary finite elements, which overcomes the challenges associated with stress singularities and complex geometries. The approach provides coarse mesh accuracy and numerical stability under incompressibility conditions, and is suitable for large scale problems that often require a large number of iterations to converge to the collapse load solution. A number of successfully solved examples, one of which has been given herein, illustrate the robustness and efficiency of the proposed method to compute the collapse load of structures

A direct mathematical programming approach for elastoplastic analysis of structures under cyclic loading

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An FE-MPEC approach for limit load evaluation in the presence of contact and displacement constraints

This paper describes a mathematical programing based approach for the direct limit load evaluation of a structural system under simultaneous contact and limited displacement conditions. The contact model we adopt can simulate either a classical unilateral (nonassociative) Coulomb friction situation or a cohesive fracture idealization at the potential discontinuity interface between contacting bodies

Mathematical programming approaches for the safety assessment of semirigid elastoplastic frames

This paper presents two complementary mathematical programming based approaches for the accurate safety assessment of semirigid elastoplastic frames under quasistatic loads. The inelastic behavior of the flexible connections and material plasticity are accommodated through piecewise linearized nonlinear yield surfaces. As is necessary for this class of structures, geometric nonlinearity is taken into account. Moreover, only a 2nd-order geometric approximation is included as this is sufficiently accurate for practical structures. The work described has a twofold contribution. First, we develop an algorithm that can robustly and efficiently process the complete (path-dependent) nonholonomic response of the structure in a stepwise (path-independent) holonomic fashion. The governing formulation is cast in mixed statickinematic variables and leads naturally to what is known in the mathematical programming literature as a mixed complementarity problem (MCP). The novelty of the proposed algorithm is that it processes the MCP directly without using some iterative (and often cumbersome) predictor-corrector procedure. Second, in the spirit of simplified analyses, the classical limit analysis approach is extended to compute the limit load multiplier under the simultaneous influence of joint flexibility, material and geometric nonlinearities, and limited ductility. Our formulation is an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints (MPEC). Various nonlinear programming based algorithms are proposed to solve the MPEC. Finally, four numerical examples, concerning practical structures and benchmark cases, are provided to illustrate application of the analyses as well as to validate the accuracy and robustness of the proposed schemes

Collapse load evaluation of structures with frictional contact supports under combined stresses

This paper extends classical limit analysis to structures for which some supports are subjected to ''nonstandard'' unilateral frictional contact with the ground. A typical and commonly adopted model is nonassociative Coulomb friction. For such cases, the use of the classical bound theorems is not possible. Moreover, simply solving the governing equations as a mixed complementarity problem (MCP) does not guarantee that the best bound has been calculated. We have therefore developed an approach that attempts to compute, in a single step, the critical (least) upper bound solution by formulating and solving an instance of the challenging class of optimization problems, known as a mathematical program with equilibrium constraints (MPEC). Two examples are provided to illustrate application of the proposed scheme, as well as to highlight some key features of such structure

Limit analysis of frames involving unilateral supports with frictional contact

Copyright © 2006 Elsevier Ltd All rights reserved.F. Tin-Loi, S. Tangaramvong and S.H. Xiahttp://www.elsevier.com/wps/find/journaldescription.cws_home/206/description#descriptio

Mechanics of Structures and Materials: Advancements and Challenges

This paper presents a hybrid uncertain static analysis for engineering structures involving stochastic and non-stochastic parameters simultaneously. In order to achieve a more generalized frameworkof analysis, the imprecise probabilistic model is implemented to represent the random variables whereas the interval analysis is adopted to model the uncertain parameters with information insufficiency. For thepurpose of illustrating the applicability of the proposed method, one multi-bay multi-storey frame structure subject to various uncertainties is investigated. In addition to the demonstration on the applicability ofthe proposed method, the well-known simulative method (i.e., Quasi-Monte-Carlo Simulation combined with Monte-Carlo Simulation (QMCS-MCS)) is also employed for verifying the computational results

Time-dependent buckling analysis of concrete-filled steel tubular arch with interval viscoelastic effects

In this paper, a finite-element-based computational method is proposed for time-dependent structural stability analysis of a concrete-filled steel tubular (CFST) arch with uncertain parameters. Specifically, the targeted uncertainty includes the mercurial effects of the creep and shrinkage of the concrete core, which inevitably affect the structural performance of the CFST arch. The structural stability of the composite arch is systematically investigated under the influence of uncertain creep and shrinkage in a time-dependent fashion. The proposed computational scheme efficiently establishes the quantitative long-term stability envelope for CFST arches against uncertain viscoelastic effects. In order to demonstrate the effectiveness and efficiency of the proposed time-dependent structural stability analysis for CFST arches, practically motivated numerical examples are thoroughly investigated throughout this work

A direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures

This paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures. Founded on a traditional finite-step formulation, our approach, however, avoids the typically cumbersome implementation of iterative predictorcorrector procedures associated with the ubiquitous return mapping algorithm. Instead, at each predefined step, the governing formulationcast in its most natural mathematical programming format known as a mixed complementarity problemis directly solved by using a complementarity solver run from within a mathematical modeling system. We have chosen the industry-standard General Algebraic Modeling System/PATH mixed complementarity problem solver that is called from within the General Algebraic Modeling System environment. We consider both von Mises and Tresca materials, with perfect or hardening (kinematic and isotropic) behaviors. Our numerical tests, five (benchmark) examples of which are presented in this paper, have been carried out using models constructed from the mixed finite element of Capsoni and Corradi (Comput. Methods Appl. Mech. Eng. 1997; 141:6793), which beneficially offers a locking-free behavior and coarse-mesh accuracy. The results indicate, in addition to an isochoric locking-free behavior, good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of Tresca yield surfaces