Gengdong Cheng

ε-relaxed approach in structural topology optimization

This paper presents a so-called ε-relaxed approach for structural topology optimization problems of discrete structures. The distinctive feature of this new approach is that unlike the typical treatment of topology optimization problems based on the ground structure approach, we eliminate the singular optima from the problem formulation and thus unify the sizing and topology optimization within the same framework. As a result, numerical methods developed for sizing optimization problems can be applied directly to the solution of topology optimization problems without any further treatment. The application of the proposed approach and its effectiveness are illustrated with several numerical examples.

STUDY ON TOPOLOGY OPTIMIZATION WITH STRESS CONSTRAINTS

Abstract The paper studies the relation between topology optimization and size optimization of truss structures. The goal of the optimization is to minimize the structural weight under stress constraints and side constraints on member cross sectional areas. The limiting stress concept is defined and the computational formula of limiting stress for truss structures calculated by a finite element method is given. Based on the limiting stress concept the continuity of the stress function at zero cross sectional area is carefully examined which enables us to understand the dilemma of defining the stress function in the closed interval up to zero cross sectional area. By considering the relation between the limiting stress and allowable stress the feasibility of stress constraints is discussed and the difficulty of adding a new bar to the truss or deleting an existing one is better understood. We have also shown that for topology optimization of truss structures the feasible design domain in the design space i...

Some aspects of truss topology optimization

The present paper studies some aspects of formulations of truss topology optimization problems. The ground structure approach-based formulations of three types of truss topology optimization problems, namely the problems of minimum weight design for a given compliance, of minimum weight design with stress constraints and of minimum weight design with stress constraints and local buckling constraints are examined. The common difficulties with the formulations of the three problems are discussed. Since the continuity of the constraint or/and objective function is an important factor for the determination of the mathematical structure of optimization problems, the issue of the continuity of stress, displacement and compliance functions in terms of the cross-sectional areas at zero area is studied. It is shown that the bar stress function has discontinuity at zero crosssectional area, and the structural displacement and compliance are continuous functions of the cross-sectional area. Based on the discontinuity of the stress function we point out the features of the feasible domain and global optimum for optimization problems with stress and/or local buckling constraints, and conclude that they are mathematical programming with discontinuous constraint functions and that they are essentially discrete optimization problems. The difference between topology optimization with global constraints such as structural compliance and that with local constraints on stress or/and local buckling is notable and has important consequences for the solution approach.

Optimal structure design with low thermal directional expansion and high stiffness

Structures with low thermal directional expansion and high stiffness have wide applications where dimensional stability is required when subject to large temperature change or thermal gradient, e.g. the supporting structure of a space camera and many other types of aero-spatial equipment. This article develops a new bi-objective structural topology optimization formulation which aims at design of structures composed of two materials with differing Youngs modulus and thermal expansion coefficients to achieve low thermal directional expansion and high stiffness. A three-phase topology optimization technique is adopted to optimize the structures. Black and white (0/1) designs are obtained by using the volume-preserving Heaviside filter and GCMMA method (globally convergent version of the method of moving asymptotes). Three structural examples are shown to illustrate how the structural supports, temperature variation and the weight factors affect the material distribution and the objectives.

Reliability-based structural optimization under hazard loads

The present paper studies the reliability-based structural optimization of the civil engineering in the seismic zone. The objective is to minimize the sum of construction material cost and the expected failure loss under severe earthquake, which is obtained by the sum of the products of the failure probability and its failure losses for the important failure modes. The set of constraints includes the deterministic constraints, and the constraints based on structural reliability—the reliability index constraints of structural element failure for the serviceability state under minor earthquake and the failure probability of the structural system for the ultimate limit state under severe earthquake. By introducing the load roughness index, the structural system reliability computation under hazard load can be greatly simplified, which is approximately determined by its weakest failure mode. Finally, the numerical example of high rising shear RC frame is calculated.

Structural shape optimization integrated with CAD environment

The research work presented here is based on the concept of the integration of optimization techniques and numerical analysis with the finite element method (FEM) and computer-aided design (CAD). A microcomputer aided optimum design system, MCADS, has been developed for general structures. Certain techniques to be discussed in the paper, e.g. the semi-analytical method for design sensitivity analysis, optimization analysis modelling for shape design, application oriented user interfaces and the coupling of automated optimization and user intervention have rendered MCADS pratical and versatile in applications for engineering structures. The above techniques and an application are presented in this paper.

New method for graded mesh generation of all hexahedral finite elements

Abstract Mapping method is widely applied by most of commercial mesh generators because of its efficiency, mesh quality. One of the obstacles to apply the mapping method and generate a graded all hexahedral mesh of high quality in an arbitrarily three-dimensional domain is the generation of hexahedral parent elements on a super-element that allows for gradations in three co-ordinate directions. This paper presents a pattern module’s method to generate the graded mesh of all hexahedral elements in a cube and thus improves the mapping method. The method requires few calculations.

New Method of Error Analysis and Detection in Semi-Analytical Sensitivity Analysis

This paper introduces a new method, the rigid-body motion test, for analysis and detection of possible abnormal errors of shape design sensitivities determined by the semi-analytical method. It is found that rigid-body rotation of an individual finite element of given type gives rise to non-vanishing semi-analytical pseudo-loads, the resultant moment of which can be applied to predict the abnormal error behaviour that has been reported for cases of semi-analytical sensitivity analysis in the literature. The proposed method is illustrated for a number of different types of elements in this paper.

Optimum Design of Pile Foundation by Automatic Grouping Genetic Algorithms

This paper studies the optimum conceptual design of pile foundations at the initial design stage. A modular method is proposed, which divides the foundation into modules and each module is identified by its characteristics of pile length, diameter, number and layout. Modules with the same characteristics may be packed and represented by a design variable. A minimum-cost optimization model with multiple design constraints based on Chinese code and a cardinality constraint is built to achieve the concurrent optimization of pile size and layout. The model is solved by the improved automatic grouping genetic algorithms to obtain the design with optimal variables and optimal variable grouping. A practical example demonstrates the effectiveness of the proposed approach.

Structural modelling and sensitivity analysis of shape optimization

It is presented in this paper that the structural modelling of shape optimization is composed of, in general cases, four distinct processes on geometry, design, analysis and perturbation models. The relationships between these models are discussed. An integrated modelling approach based on geometric shape parameterization and automatic mesh generation is proposed. In cooperation with this modelling approach, the semi-analytic sensitivity analysis has been effectively employed. These techniques join shape optimization with FEM and CAD packages and apply it versatilely to optimum designs of general structures. The implementation and applications of the integrated modelling approach and semi-analytic sensitivity analysis to shape optimization of structures with coupling of stress and temperature fields are illustrated.