Topology Design Of Continuum Structures Research Articles

LiteITD a MATLAB Graphical User Interface (GUI) program for topology design of continuum structures

Over the past few decades, topology optimization has emerged as a powerful and useful tool for the design of structures, also exploiting the ever growing computational speed and power. The design process has also been affected by computers which changed the concept of form into the concept of formation and the emergence of digital design. Topology optimization can modify existing designs, incorporate explicit features into a design and generate completely new designs. This paper will show how topology optimization can be used as a digital tool. The liteITD (lite version of Isolines Topology Design) software package will be described with the purpose of providing a tool for topology design. The liteITD program solves the topology optimization of two-dimensional continuum structures using von Mises stress isolines under single or multiple loading conditions, with different material properties in tension and compression, and multiple materials. The liteITD program is fully implemented in the MATrix LABoratory (MATLAB) software environment of MathWorks under Windows operating system. GUIDE (Graphical User Interface Development Environment) was used to create a friendly Graphical User Interface (GUI). The usage of this application is directed to students mainly (educational purposes), although also to designers and engineers with experience. The liteITD program can be downloaded and used for free from the website: http://www.upct.es/goe/software/liteITD.php.

Optimal topology design of continuum structures with stress concentration alleviation via level set method

SUMMARYAlthough the phenomenon of stress concentration is of paramount importance to engineers when they are designing load‐carrying structures, stiffness is often used as the solely concerned objective or constraint functional in the studies of optimal topology design of continuum structures. Sometimes this will lead to optimal designs with severe stress concentrations that may be highly responsible for the fracture, creep, and fatigue of structures. The aim of the present work is to develop some effective numerical techniques for designing stiff structures with less stress concentrations. This is achieved by introducing some specific stress measures, which are sensitive to the existence of high local stresses, in the problem formulation and resolving the corresponding optimization problem numerically in a level set framework. Our study indicates that with use of the proposed numerical schemes, some intrinsic difficulties in stress‐related topology optimization of continuum structures can be overcome in a natural way. Copyright © 2012 John Wiley & Sons, Ltd.

Performance-Based Optimization: A Review

The performance-based optimization (PBO) method has recently been developed for topology design of continuum structures with stress, displacement and mean compliance constraints. The PBO method incorporates the finite element analysis, modern structural optimization theory and performance-based design concepts into a single scheme to automatically generate optimal designs of continuum structures. Performance indices are used to monitor the performance optimization history of topologies while performance-based optimality criteria are employed to identify the optimum from the optimization process. The performance characteristics of a structure in an optimization process are fully captured. The PBO technique allows the designer to tailor the design to a specific performance level required by the owner. This paper reviews the state-of-the-art development of automated performance-based optimal design techniques for topology design of continuum structures. Several practical design examples are provided to demonstrate the effectiveness and validity of the PBO technology as an advanced design tool.

Topological optimization of continuum structures with design-dependent surface loading ? Part I: new computational approach for 2D problems

This paper describes a new computational approach for optimum topology design of 2D continuum structures subjected to design-dependent loading. Both the locations and directions of the loads may change as the structural topology changes. A robust algorithm based on a modified isoline technique is presented that generates the appropriate loading surface which remains on the boundary of potential structural domains during the topology evolution. Issues in connection with tracing the variable loading surface are discussed and treated in the paper. Our study indicates that the influence of the variation of element material density is confined within a small neighbourhood of the element. With this fact in mind, the cost of the calculation of the sensitivities of loads may be reduced remarkably. Minimum compliance is considered as the design problem. There are several models available for such designs. In the present paper, a simple formulation with weighted unit cost constraints based on the expression of potential energy is employed. Compared to the traditional models (i.e., the SIMP model), it provides an alternative way to implement the topology design of continuum structures. Some 2D examples are tested to show the differences between the designs obtained for fixed, design-independent loading, and for variable, design-dependent loading. The general and special features of the optimization with design-dependent loads are shown in the paper, and the validity of the algorithm is verified. An algorithm dealing with 3D design problems is described in Part II, which is developed from the 2D algorithm in the present Part I of the paper.

Topology design of structures using a dual algorithm and a constraint on the perimeter

AbstractDual optimization algorithms are well suited for the topology design of continuum structures in discrete variables, since in these problems the number of constraints is small in comparison to the number of design variables. The ‘raw’ dual algorithm, which was originally proposed for the minimum compliance design problem, worked well when a perimeter constraint was added in addition to the volume constraint. However, if the perimeter constraint was gradually relaxed by increasing the upper bound on the allowable perimeter, the algorithm tended to behave erratically. Recently, a simple strategy has been suggested which modifies the raw dual algorithm to make it more robust in the absence of the perimeter constraint; in particular the problem of checkerboarding which is frequently observed with the use of lower‐order finite elements is eliminated. In this work, we show how the perimeter constraint can be incorporated in this improved algorithm, so that it not only provides a designer with a control over the topology, but also generates good topologies irrespective of the value of the upper bound on the perimeter. Copyright © 2002 John Wiley & Sons, Ltd.

Recent developments in topology design of materials and mechanisms

esente des exemples de conception de m´ ecanismes fle xibles. Mots clOptimisation topologique, microstructures, mfle xibles. Abstract. This paper gives a brief introduction to some of the methods used in topology design of continuum structures and to their use for the design of materials and mechanisms. This encompasses the use of topology design in design of materials with extreme properties, and the introduction of buckling criteria in such design problems. A topic is also the design of isotropic composites which realize certain popular interpolation schemes used in topology design (making the dog bite its tail). Finally, examples of the design of fle xible mechanisms will be discussed.

A performance-based optimization method for topology design of continuum structures with mean compliance constraints

A performance-based optimization (PBO) method for optimal topology design of linear elastic continuum structures with mean compliance constraints is presented in this paper. The performance-based design concept is incorporated in continuum topology optimization, which is treated as the problem of improving the performance of a continuum design domain in terms of the efficiency of material usage and overall stiffness. A simple scheme is employed in the proposed method to suppress the formation of checkerboard patterns. Two energy-based performance indices are derived for quantifying the topology performance of plane stress structures and plates in bending. Performance-based optimality criteria incorporating performance indices are proposed, and can be used in any continuum topology optimization methods for compliance minimization problems to obtain the optimum. Numerical examples are provided to demonstrate the effectiveness and validity of the PBO method in producing optimal topologies of continuum structures.

A method for treating damage related criteria in optimal topology design of continuum structures

In this paper we present a formulation of the wellknown structural topology optimization problem that accounts for the presence of loads capable of causing permanent damage to the structure. Damage is represented in the form of an internal variable model which is standard in continuum damage mechanics. Here we employ an interpretation of this model as an optimum remodeling problem for maximal compliance over all damage distributions, making also the analysis of the damage model a study in structural optimization. The damage criterion can be included in the optimal design model in a number of ways. We present results for finding the optimal topology of the reinforcement of an existing design with the goal of minimizing damage. Also, we treat the problem of finding the topology of a structure where we seek maximal stiffness under service loads with a constraint on the amount of damage which occurs under a separate set of damage loads.

A method for treating damage related criteria in optimal topology design of continuum structures

A method for treating damage related criteria in optimal topology design of continuum structures