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Article
Publication date: 1 January 2006

R. Balamurugan, C.V. Ramakrishnan and N. Swaminathan

The structural design problem can be viewed as an iterative design loop with each iteration involving two stages for topology and shape designs with genetic algorithm (GA) as the…

Abstract

Purpose

The structural design problem can be viewed as an iterative design loop with each iteration involving two stages for topology and shape designs with genetic algorithm (GA) as the optimization tool for both.

Design/methodology/approach

The topology optimization problem, which is ill posed, is regularized using a constraint on perimeter and solved using GA. The problem is formulated as one of compliance minimization subject to volume constraint for the single loading case. A dual formulation of this has been used for the multiple loading cases resulting in as many behavioral constraints as there are loading cases. The tentative topology given by the topology optimization module is taken and the domain boundary is approximated using straight lines, B‐splines and cubic spline curves and design variables are selected among the boundary defining points. Optimum boundary shape of the problem has been obtained using GA in two different ways: without stress constraints; and with stress constraints.

Findings

The proposed two stage strategy has been tested on benchmark structural optimization problems and its performance is found to be extremely good.

Practical implications

The strategy appears to be eminently suitable for implementation in a general purpose FE software as an add‐on module for structural design optimization.

Originality/value

It has been observed that the integrated topology and shape design method is robust and easy to implement in comparison with other techniques. The computing time requirements for the GA does not appear daunting in the present scenario of high performance parallel computing and improved GA techniques.

Details

Engineering Computations, vol. 23 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 29 June 2020

Wenming Cheng, Hui Wang, Min Zhang and Run Du

The purpose of this paper is to propose an improved proportional topology optimization (IPTO) algorithm for tackling the stress-constrained minimum volume optimization problem…

Abstract

Purpose

The purpose of this paper is to propose an improved proportional topology optimization (IPTO) algorithm for tackling the stress-constrained minimum volume optimization problem, which can meet the requirements that are to get rid of the problems of numerical derivation and sensitivity calculation involved in the process of obtaining sensitivity information and overcome the drawbacks of the original proportional topology optimization (PTO) algorithm.

Design/methodology/approach

The IPTO algorithm is designed by using the new target material volume update scheme and the new density variable update scheme and by introducing the improved density filter (considering the weighting function based on the Gaussian distribution) and Heaviside-type projection operator on the basis of the PTO algorithm. The effectiveness of the IPTO algorithm is demonstrated by solving the stress-constrained minimum volume optimization problems for two numerical examples and being compared with the PTO algorithm.

Findings

The results of this paper show that the uses of the proposed strategies contribute to improving the optimized results and the performance (such as the ability to obtain accurate solutions, robustness and convergence speed) of the IPTO algorithm. Compared with the PTO algorithm, the IPTO algorithm has the advantages of fast convergence speed, enhancing the ability to obtain accurate solutions and improving the optimized results.

Originality/value

This paper achieved the author’s intended purpose and provided a new idea for solving the stress-constrained optimization problem under the premise of avoiding obtaining sensitivity information.

Details

Engineering Computations, vol. 38 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 July 2014

Diego Esteves Campeão, Sebastian Miguel Giusti and Andre Antonio Novotny

– The purpose of this paper is to compare between two methods of volume control in the context of topological derivative-based structural optimization of Kirchhoff plates.

Abstract

Purpose

The purpose of this paper is to compare between two methods of volume control in the context of topological derivative-based structural optimization of Kirchhoff plates.

Design/methodology/approach

The compliance topology optimization of Kirchhoff plates subjected to volume constraint is considered. In order to impose the volume constraint, two methods are presented. The first one is done by means of a linear penalization method. In this case, the penalty parameter is the coefficient of a linear term used to control the amount of material to be removed. The second approach is based on the Augmented Lagrangian method which has both, linear and quadratic terms. The coefficient of the quadratic part controls the Lagrange multiplier update of the linear part. The associated topological sensitivity is used to devise a structural design algorithm based on the topological derivative and a level-set domain representation method. Finally, some numerical experiments are presented allowing for a comparative analysis between the two methods of volume control from a qualitative point of view.

Findings

The linear penalization method does not provide direct control over the required volume fraction. In contrast, through the Augmented Lagrangian method it is possible to specify the final amount of material in the optimized structure.

Originality/value

A strictly simple topology design algorithm is devised and used in the context of compliance structural optimization of Kirchhoff plates under volume constraint. The proposed computational framework is quite general and can be applied in different engineering problems.

Details

Engineering Computations, vol. 31 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 20 April 2015

Saeed Maleki Jebeli and Masoud Shariat Panahi

The purpose of this paper is to introduce an evolutionary heuristic method for simultaneous optimization of topology and material property distribution of functionally graded (FG…

Abstract

Purpose

The purpose of this paper is to introduce an evolutionary heuristic method for simultaneous optimization of topology and material property distribution of functionally graded (FG) structures under a prescribed loading condition.

Design/methodology/approach

The proposed procedure is inspired by heuristic nature of bi-directional evolutionary structural optimization (BESO) and genetic algorithm (GA). The optimization algorithm is developed in the context of minimum compliance (maximum stiffness) design problem. The problem is modeled by means of finite element method (FEM). The element-wise material volume fractions and elements’ status (i.e. existence or nonexistence in FE model) are introduced as design variables. After FE analysis, sensitivities are obtain and filtered according to BESO. Having determined sensitivities, by means of a heuristic scheme combined by GA, topology and material property distribution for the next cycle of optimization are determined by updating design variables.

Findings

The adopted method has been tested by means of several examples previously reported in literature. The comparison showed the superiority of the proposed method against its rival in terms of relative reduction in compliance, smoother material property distribution and computational cost.

Originality/value

The value of the described method lies in its simple (yet efficient) nature. In contrast with its only rival in literature which more relied on mathematical approach, proposed method uses a series of logic-based heuristic ideas to drive reasonable solutions but with far less computational cost.

Details

Engineering Computations, vol. 32 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 April 2014

Dong Zhou, Xu Jia, Chuan Lv and Le Kang

Maintainability, as an intrinsic property that shows how well a product can be maintained, should be strictly controlled in the design stage. Maintenance space is an important…

Abstract

Purpose

Maintainability, as an intrinsic property that shows how well a product can be maintained, should be strictly controlled in the design stage. Maintenance space is an important aspect of maintainability and should be verified in the design stage. Methods to verify maintenance space based on expert knowledge or vision cone have been proposed. However, no proper quantitative solutions have been proposed yet to verify maintenance space in the design stage. This paper aims to provide a new method to evaluate quantitatively the maintenance space in a virtual environment by using the swept volume (SV).

Design/methodology/approach

An integrated platform for quantitatively evaluating maintenance space in a virtual environment is designed. Virtual reality technology and digital prototype are used to overcome the shortage of physical prototypes in the design stage. SVs are applied to represent the movement of the hand along the entire maintenance process. Maintenance operations are divided into three basic types. Each type of basic operation refers to two quantitative indexes, namely the surface area and the volume of the SV of the maintenance personnel. Data on the indexes are gathered and calculated to evaluate maintenance space.

Findings

The proposed methodology can evaluate feasibly and efficiently the maintenance space determined by the layout design of product components in the design stage.

Practical implications

Application of the proposed method can help designers reduce the shortness of maintenance space and improve the design layout of products.

Originality/value

A method to evaluate maintenance space that employs a quantitative combination of virtual environment and swept volume is pressed.

Details

Assembly Automation, vol. 34 no. 2
Type: Research Article
ISSN: 0144-5154

Keywords

Article
Publication date: 7 May 2020

Jéderson da Silva, Jucélio Tomás Pereira and Diego Amadeu F. Torres

The purpose of this paper is to propose a new scheme for obtaining acceptable solutions for problems of continuum topology optimization of structures, regarding the distribution…

Abstract

Purpose

The purpose of this paper is to propose a new scheme for obtaining acceptable solutions for problems of continuum topology optimization of structures, regarding the distribution and limitation of discretization errors by considering h-adaptivity.

Design/methodology/approach

The new scheme encompasses, simultaneously, the solution of the optimization problem considering a solid isotropic microstructure with penalization (SIMP) and the application of the h-adaptive finite element method. An analysis of discretization errors is carried out using an a posteriori error estimator based on both the recovery and the abrupt variation of material properties. The estimate of new element sizes is computed by a new h-adaptive technique named “Isotropic Error Density Recovery”, which is based on the construction of the strain energy error density function together with the analytical solution of an optimization problem at the element level.

Findings

Two-dimensional numerical examples, regarding minimization of the structure compliance and constraint over the material volume, demonstrate the capacity of the methodology in controlling and equidistributing discretization errors, as well as obtaining a great definition of the void–material interface, thanks to the h-adaptivity, when compared with results obtained by other methods based on microstructure.

Originality/value

This paper presents a new technique to design a mesh made with isotropic triangular finite elements. Furthermore, this technique is applied to continuum topology optimization problems using a new iterative scheme to obtain solutions with controlled discretization errors, measured in terms of the energy norm, and a great resolution of the material boundary. Regarding the computational cost in terms of degrees of freedom, the present scheme provides approximations with considerable less error if compared to the optimization process on fixed meshes.

Article
Publication date: 1 May 1992

E. HINTON, N.V.R. RAO and J. SIENZ

This paper deals with structural shape and thickness optimization of axisymmetric shell structures loaded symmetrically. In the finite element stress analysis use is made of newly…

Abstract

This paper deals with structural shape and thickness optimization of axisymmetric shell structures loaded symmetrically. In the finite element stress analysis use is made of newly developed linear, quadratic, and cubic, variable thickness, C(0) elements based on axisymmetric Mindlin‐Reissner shell theory. An integrated approach is used to carry out the whole shape optimization process in a fully automatic manner. A robust, versatile and flexible mesh generator is incorporated with facilities for generating either uniform or graded meshes, with constant, linear, or cubic variation of thickness, pressure etc. The midsurface geometry and thickness variations of the axisymmetric shell structure are defined using cubic splines passing through certain key points. The design variables are chosen as the coordinates and/or the thickness at the key points. Variable linking procedures are also included. Sensitivity analysis is carried out using either a semi‐analytical method or a global finite difference method. The objective of the optimization is the weight minimization of the structure. Several examples are presented illustrating optimal shapes and thickness distributions for various shells. The changes in the bending, membrane and shear strain energies during the optimization process are also monitored.

Article
Publication date: 30 September 2014

Kun Cai, Zhen Luo and Qing H. Qin

The purpose of this paper is to develop a heuristic method for topology optimization of a continuum with bi-modulus material which is frequently occurred in practical engineering…

Abstract

Purpose

The purpose of this paper is to develop a heuristic method for topology optimization of a continuum with bi-modulus material which is frequently occurred in practical engineering.

Design/methodology/approach

The essentials of this model are as follows: First, the original bi-modulus is replaced with two isotropic materials to simplify structural analysis. Second, the stress filed is adopted to calculate the effective strain energy densities (SED) of elements. Third, a floating reference interval of SED is defined and updated by active constraint. Fourth, the elastic modulus of an element is updated according to its principal stresses. Final, the design variables are updated by comparing the local effective SEDs and the current reference interval of SED.

Findings

Numerical examples show that the ratio between the tension modulus and the compression modulus of the bi-modulus material in a structure has a significant effect on the final topology design, which is different from that in the same structure with isotropic material. In the optimal structure, it can be found that the material points with the higher modulus are reserved as much as possible. When the ratio is far more than unity, the material can be considered as tension-only material. If the ratio is far less than unity, the material can be considered as compression-only material. As a result, the topology optimization of continuum structures with tension-only or compression-only materials can also be solved by the proposed method.

Originality/value

The value of this paper is twofold: the bi-modulus material layout optimization in a continuum can be solved by the method proposed in this paper, and the layout difference between the structure with bi-modulus material and the same structure but with isotropic material shows that traditional topology optimization result could not be suitable for a real bi-modulus layout design project.

Details

Engineering Computations, vol. 31 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 June 2005

S.M.B. Afonso, J. Sienz and F. Belblidia

Shells are widely used structural systems in engineering practice. These structures have been used in the civil, automobile and aerospace industries. Many shells are designed…

1188

Abstract

Purpose

Shells are widely used structural systems in engineering practice. These structures have been used in the civil, automobile and aerospace industries. Many shells are designed using the finite element analysis through the conventional and costly trial and error scheme. As a more efficient alternative, optimization procedures can be used to design economic and safe structures.

Design/methodology/approach

This paper presents developments, integration and applications of reliable and efficient computational tools for the structural optimization of variable thickness plates and free‐form shells. Topology, sizing and shape optimization procedures are considered here. They are applied first as isolated subjects. Then these tools are combined to form a robust and reliable fully integrated design optimization tool to obtain optimum designs. The unique feature is the application of a flexible integrally stiffened plate and shell formulation to the design of stiffened plates and shells.

Findings

This work showed the use of different optimization strategies to obtain an optimal design for plates and shells. Both topology optimization (TO) and structural shape optimization procedures were considered. These two optimization applications, as separate procedures produce new designs with a great improvement when compared to the initial designs. However, the combination of stiffening TO and sizing optimization using integrally stiffened shells appears as a more attractive tool to be used. This was illustrated with several examples.

Originality/value

This work represents a novel approach to the design of optimally stiffened shells and overcomes the drawbacks of both topology optimization and structural shape optimization procedures when applied individually. Furthermore, the unique use of integrally stiffened shell elements for optimization, unlike conventional shell‐stiffening optimization techniques, provided a general and extremely flexible tool.

Details

Engineering Computations, vol. 22 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 24 August 2021

Mohamed Abdelhamid and Aleksander Czekanski

This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. The authors trace the different sources of…

Abstract

Purpose

This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. The authors trace the different sources of non-convexification in the context of topology optimization problems starting from domain discretization, passing through penalization for discreteness and effects of filtering methods, and end with a note on continuation methods.

Design/methodology/approach

Starting from the global optimum of the compliance minimization problem, the authors employ analytical tools to investigate how intermediate density penalization affects the convexity of the problem, the potential penalization-like effects of various filtering techniques, how continuation methods can be used to approach the global optimum and how the initial guess has some weight in determining the final optimum.

Findings

The non-convexification effects of the penalization of intermediate density elements simply overshadows any other type of non-convexification introduced into the problem, mainly due to its severity and locality. Continuation methods are strongly recommended to overcome the problem of local minima, albeit its step and convergence criteria are left to the user depending on the type of application.

Originality/value

In this article, the authors present a comprehensive treatment of the sources of non-convexity in density-based topology optimization problems, with a focus on linear elastic compliance minimization. The authors put special emphasis on the potential penalization-like effects of various filtering techniques through a detailed mathematical treatment.

Details

Engineering Computations, vol. 39 no. 3
Type: Research Article
ISSN: 0264-4401

Keywords

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