S. Tangaramvong

Dynamic analysis and reliability assessment of structures with uncertain-but-bounded parameters under stochastic process excitations

This paper presents the non-deterministic dynamic analysis and reliability assessment of structures with uncertain-but-bounded parameters under stochastic process excitations. Random ground acceleration from earthquake motion is adopted to illustrate the stochastic process force. The exact change ranges of natural frequencies, random vibration displacement and stress responses of structures are investigated under the interval analysis framework. Formulations for structural reliability are developed considering the safe boundary and structural random vibration responses as interval parameters. An improved particle swarm optimization algorithm, namely randomised lower sequence initialized high-order nonlinear particle swarm optimization algorithm, is employed to capture the better bounds of structural dynamic characteristics, random vibration responses and reliability. Three numerical examples are used to demonstrate the presented method for interval random vibration analysis and reliability assessment of structures. The accuracy of the results obtained by the presented method is verified by the randomised Quasi-Monte Carlo simulation method (QMCSM) and direct Monte Carlo simulation method (MCSM).

Robust fuzzy structural safety assessment using mathematical programming approach

This paper presents a robust safety assessment for engineering structures involving fuzzy uncertainties. Uncertain applied loads and yielding capacities of structural elements are modelled as fuzzy variables with associated membership functions representing possibility distributions. A new computation-orientated methodology, namely the α-level collapse assessment (α-level CA) approach, is developed to provide structural safety profile by constructing membership function of the structural collapse load limit accommodating fuzzy uncertainties. The proposed method firstly utilizes the α-level strategy to transform the fuzzy limit analysis into a series of interval limit analyses. By implementing the concept of robust and optimistic optimizations, a mathematical programming (MP) scheme is proposed to explicitly capture the upper and lower bounds of the collapse load limit at each α-sublevel. Subsequently, the membership function of the collapse load limit is established by using the upper and lower bounds obtained from the series of α-sublevel calculations. The proposed α-level mathematical programming scheme preserves the quality of sharpness of the bounds of collapse load limit at each α-sublevel, which consequently provides a rigorous evaluation on the fuzzy profile of the safety of engineering structures against structural collapse. Numbers of numerical examples, motivated by real-world engineering applications, have been investigated to illustrate the accuracy, efficiency and applicability of the proposed method.

Time-Dependent Buckling Analysis of Concrete-Filled Steel Tubular Arch with Interval Viscoelastic Effects

AbstractIn 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 paramet...

Optimal Performance-Based Rehabilitation of Steel Frames Using Braces

AbstractThis paper presents a mathematical programming–based approach for optimal retrofitting of steel structures with braces, subject to some given system performance criteria. The aim is to ensure the safety of the post-retrofitted structures under applied forces and limited displacement conditions. The proposed scheme uses a simple form of the classical ground structure–type concept to accommodate possible brace locations. Three rehabilitation cases are studied, each of which is formulated as an instance of a nonconvex and nonsmooth optimization problem generally referred to as a mathematical program with equilibrium constraints or MPEC. In spite of the fact that this type of problem is known to be challenging to solve in the mathematical programming literature, a simple, efficient, and robust approach to process is proposed. The system performance of all retrofitted structures is validated using exact nonholonomic evolutive analyses.

Influence of Interval Uncertainty on the Behavior of Geometrically Nonlinear Elastoplastic Structures

AbstractThis paper proposes an interval analysis scheme to map out the complete bound spectrum of the most maximum and most minimum responses of geometrically nonlinear elastoplastic structures subjected to both interval applied loads and interval inelastic material properties. The proposed heuristic method uses a finite-step holonomic formulation under pseudodisplacement control. Geometric nonlinearity is modeled using a conventional second-order approximation. The analysis thus determines directly the most maximum and most minimum bound solutions by processing a pair of optimization problems, known as interval mathematical programs with equilibrium constraints or interval MPECs. The simultaneous presence of complementarity constraints and interval data is the main cause of difficulties (associated with nonconvex and/or nonsmooth optimization programs) underpinning the interval MPECs considered. The simple solution approach proposed reformulates the interval MPECs into their noninterval nonlinear program...

Interval Limit Analysis of Rigid Perfectly Plastic Structures

AbstractThis article presents a novel extended limit analysis approach that determines the sharp maximum and minimum bounds on the collapse load of rigid perfectly plastic structures simultaneously subject to uncertain but bounded loading magnitudes and plastic material capacities. The governing formulation is cast as a linear programming problem with interval coefficients. Linearity is achieved by a suitable piecewise linearization of nonlinear yield surfaces. The proposed algorithm is founded on a characteristic formula concept and an appropriate interval arithmetic interpretation to transform the interval limit analysis problem into two deterministic linear programming problems that can be solved by any available linear programming solver.

A Complementarity Approach for Elastoplastic Analysis of Frames with Uncertainties

Traditional elastoplastic analysis presumes that all structural data are known exactly. However, these values often cannot be predicted precisely: they are influenced by such factors as manufacturing errors, material defects, and environmental changes. Ignoring these may lead to inaccurate (overly conservative or nonconservative) results. It is thus important that the effects of uncertain data be quantified in a reliable assessment of structural safety. This paper presents the elastoplastic analysis of skeletal frames with uncertaintiesassumed to be interval quantities (i.e. with known upper and lower bounds). Starting from the well-known mixed complementarity program (MCP) statement of the state problem without uncertainties, we extend this to an optimisation problem formulation involving complementarity constraints (that represent the plastic nature of the ductile material). Calculations for both upper and lower bounds of displacements corresponding to monotonically increasing loads are computed. The final results are checked through a comparison with interval limit analyses and Monte Carlo simulations.

Interval Limit Analysis Within a Scaled Boundary Element Framework

The paper proposes a novel approach for the interval limit analysis of rigid-perfectly plastic structures with (nonprobabilistic) uncertain but bounded forces and yield capacities that vary within given continuous ranges. The discrete model is constructed within a polygon-scaled boundary finite element framework, which advantageously provides coarse mesh accuracy even in the presence of stress singularities and complex geometry. The interval analysis proposed is based on a so-called convex model for the direct determination of both maximum and minimum collapse load limits of the structures involved. The formulation for this interval limit analysis takes the form of a pair of optimization problems, known as linear programs with interval coefficients (LPICs). This paper proposes a robust and efficient reformulation of the original LPICs into standard nonlinear programming (NLP) problems with bounded constraints that can be solved using any NLP code. The proposed NLP approach can capture, within a single step, the maximum collapse load limit in one case and the minimum collapse load limit in the other, and thus eliminates the need for any combinatorial search schemes.

Interval Limit Analysis of Structures with Uncertain but Non-probabilistic Applied Forces

This paper extends the scope of classical limit analysis to incorporate the influence of uncertain, but still non-probabilistic, applied forces that can vary independently within specified ranges. We focus on the use of interval analysis or socalled “convex” model in determining the two extreme (maximum and minimum) bounds to the collapse load limit of ductile rigid perfectly plastic structures. The formulation for the interval limit analysis uses the well-known piecewise linear yield concept, and can be formulated as a challenging form of optimization programs, known as a linear program with interval coefficients (LPIC). We propose a novel reformulation of the original LPIC into a standard nonlinear programming (NLP) problem with bounded constraints that can be solved using any NLP code. The proposed NLP approach can efficiently and robustly capture, within a single step, the maximum collapse load limit in one case and the minimum collapse load limit in the other, and thus eliminates the need for any combinatorial search schemes.

Optimal Retrofitting of Structures Using Braces

The paper presents a mathematical programming based approach for the efficient retrofitting, with braces, of structures subjected to multiple load cases and serviceability limitations, simultaneously. The method is based on a simple ground structure concept that generates within a design domain all possible cross braces, and then automates the decision as to which brace members are retained or eliminated using unknown 0-1 variables. The optimization minimizes simultaneously the total number and volume of design braces. The governing problem takes the form of a disjunctive and combinatorial optimization program, cast as a mixed integer nonlinear programming (MINLP) problem. We propose a two-step optimization algorithm to solve the MINLP, in which the first step processes a standard nonlinear programming (NLP) problem by relaxing the binary variables to a continuous bounded system, the results of which form an initial basis for the second and final solve of the MINLP problem with binary variables.