Showing papers by "Grant P. Steven published in 1999"
TL;DR: In this paper, an extension of the method called bidirectional evolutionary structural optimization (BESO) for topology optimization subject to stiffness and displacement constraints is presented, which allows for the material to be added as well as to be removed to modify the structural topology.
Abstract: Evolutionary structural optimization (ESO) method was originally developed based on the idea that by systematically removing the inefficient material, the residual shape of the structure evolves toward an optimum. This paper presents an extension of the method called bidirectional ESO (BESO) for topology optimization subject to stiffness and displacement constraints. BESO allows for the material to be added as well as to be removed to modify the structural topology. Basic concepts of BESO including the sensitivity number and displacement extrapolation are proposed and optimization procedures are presented. Integrated with the finite element analysis technique, BESO is applied to several two-dimensional plane stress problems. Its effectiveness and efficiency are examined in comparison with the results obtained by ESO. It is found that BESO is more reliable and computationally more efficient than ESO in most cases. Its capability and limitation are discussed.
272 citations
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01 Jan 1999
TL;DR: In this paper, the authors present a technique for stress analysis and strength prediction for transverse stitching and apply it in a variety of applications, e.g., failure criteria, optimal design, and damage tolerance.
Abstract: Preface. 1. Introduction. 2. Stress Analysis Techniques. 3. Failure Criteria and Strength Prediction. 4. Damage Tolerance. 5. Optimum Design. 6. Effect of Transverse Stitching. 7. Selected Applications. References. Index.
244 citations
TL;DR: This extension incorporates an evolutionary iterative process into finite element heat solutions into shape and topology design problems subjected to steady heat conduction.
198 citations
TL;DR: In this paper, a methodology was developed (and integrated into the Evolutionary Structural Optimization (ESO) program EVOLVE) which produced the optimal 3D finite element models of a structure in a more reliable way than the traditional ESO method.
Abstract: Evolutionary Structural Optimization (ESO), is a numerical method of structural optimization that is integrated with finite element analysis (FEA). Bi-directional ESO (BESO) is an extension to this method and can begin with minimal amount of material (only that necessary to support the load and support cases) in contrast to ESO which uses an initially oversized structure. Using BESO the structure is then allowed to grow into the optimum design or shape by both adding elements where the stresses are the highest and taking elements away where stresses are the lowest. In conducting this research, a methodology was developed (and integrated into the ESO program EVOLVE) which produced the optimal 3D finite element models of a structure in a more reliable way than the traditional ESO method. Additionally, the BESO method was successfully extended to multiple load cases for both 2D and 3D. Two different algorithms were used to find the best structure experiencing more than one load case and the results of each are included.
114 citations
TL;DR: In this paper, the contours of element von Mises stress and stiffness sensitivity number are found to be very similar in finite element analysis (FEA), and it is concluded that the optimized topologies of a structure using the fully stressed criterion and the minimum compliance or maximum stiffness criterion are equivalent.
Abstract: In a finite element analysis (FEA), the contours of element von Mises stress and stiffness sensitivity number are found to be very similar. This paper shows there to be an equivalence between the von Mises stress criterion and the stiffness criterion for element elimination or addition in evolutionary structural optimization. The examples presented demonstrate the same resulting topologies during the evolving process using the two “different” criteria. The effect of numerical errors on topology is also investigated. It is concluded that the optimized topologies of a structure using the fully stressed criterion and the minimum compliance or maximum stiffness criterion are equivalent.
84 citations
TL;DR: In this paper, the evolutionary structural optimization method is further developed to deal with thermoelastic optimization, where structural material is progressively redistributed so as to minimize the displacement under thermal and mechanical loading.
79 citations
TL;DR: In this paper, a theoretical formulation to model composite beam smart structures in which the piezoelectric actuators and sensors are treated as constituent parts of the entire structural system is presented, based on a high order displacement field coupled with a layerwise linear electric potential.
Abstract: A theoretical formulation to model composite smart structures in which the piezoelectric actuators and sensors are treated as constituent parts of the entire structural system is presented here. The mathematical model is based on a high order displacement field coupled with a layerwise linear electric potential. This model is developed for a composite beam structure using Hamilton's variational principle and is facilitated by the finite element (FE) formulation. The generic element implemented in the FE analysis is a two-noded Hermitian - 2(n+1) layerwise noded element for an n-layered beam. The variational principle led to a derivation that could include dynamic analysis but the present work will only focus on the static beam structure. This formulation in general will enable the modeling of vibration and shape control applications. Comparison of numerical results from this formulation with previous works, including three configurations - non-piezoelectric, actuator and sensor configurations, showed a high to a reasonable degree of correlation. The effects of varying actuator locations and orientations on the deflection and curvature of the beam were also studied.
75 citations
TL;DR: In this paper, an evolutionary structural optimization (ESO) method is proposed for structural topology optimization subject to frequency constraints, which is based on the idea that by gradually removing inefficient material, the residual shape of structure evolves toward an optimum.
Abstract: This paper presents an evolutionary method for structural topology optimization subject to frequency constraints. The evolutionary structural optimization (ESO) method is based on the idea that by gradually removing inefficient material, the residual shape of structure evolves toward an optimum. The method is further developed by allowing the material to be added as well as removed, and this new approach is called the bidirectional ESO method (BESO). BESO has been successfully used for problems of stress and stiffness/displacement constraints. Its application to frequency optimization is addressed in this paper. Three kinds of optimization objectives, namely, maximizing a single frequency, maximizing multiple frequencies, and designing structures with prescribed frequencies are considered. Four examples are tested by BESO and ESO. The objective functions yielded by the two methods are close, and BESO is computationally more efficient in most cases.
68 citations
TL;DR: In this article, a laminate block modeling approach for 3D through-the-thickness angle interlock woven composites is used to develop one finite element analysis (FEA) model and two analytical models, namely the ZXY model and the ZYX model.
Abstract: In this paper, a laminate block modeling approach for three-dimensional (3D) through-the-thickness angle interlock woven composites is used to develop one finite element analysis (FEA) model and two analytical models, namely the “ZXY model” and the “ZYX model”. These models can be used to determine the mechanical properties and the coefficients of thermal expansion for 3D through-the-thickness angle interlock woven composites. A parametric study shows that there is good agreement between these FEA and analytical models. The parametric study also demonstrates the effects of the fiber volume fraction of the warp weaver (i.e., z yarn) and the space between two adjacent filler yarns on the mechanical properties and the coefficients of thermal expansion. Finally, the present models are found to correlate reasonably well with the predicted and measured results available in the literature.
66 citations
01 Aug 1999
TL;DR: In this article, a performance index is developed for evaluating the efficiency of structural topologies based on the scaling design approach, which is incorporated in the evolutionary structural optimization (ESO) method to monitor the optimization process when gradually removing inefficient material from the structure.
Abstract: This paper presents a method for assisting the optimal selection of topologies for the minimum-weight design of continuum structures subject to stress constraints by using the performance index (PI). A performance index is developed for evaluating the efficiency of structural topologies based on the scaling design approach. This performance index is incorporated in the evolutionary structural optimization (ESO) method to monitor the optimization process when gradually removing inefficient material from the structure. The optimal topology can be identified from the performance index history. Various structures with stress and height constraints are investigated by using this performance index, which is also employed to compare the efficiency of structural topologies generated by different optimization methods. It is shown that the proposed performance index is capable of measuring the efficiency of structural topologies obtained by various structural optimization methods and is a valuable design tool for engineers in selecting optimal topologies in structural design.
58 citations
TL;DR: In this paper, two models for plain weave composites are presented for elastic constants, namely, sinusoidal yarn model, and analytical model for failure strengths, which are generated by interfacing an in-house computer code with FEA software strand6.
TL;DR: In this paper, unit cell and laminate modeling approaches were developed for predicting the effective elastic constants of three-dimensional (3D) orthogonal woven fabric composites, for both models...
Abstract: Unit cell and laminate modeling approaches were previously developed for predicting the effective elastic constants of three-dimensional (3D) orthogonal woven fabric composites [1]. For both models...
TL;DR: Numerical results indicate that the incorporation of tension/compression material is very effective in achieving tension- and compression-dominated designs, which has produced the structural shapes that make the best utilisation of the available materials.
Abstract: The Evolutionary Structural Optimisation (ESO) method is based on the simple concept that by slowly removing inefficiently used material from an over-designed structure, the residual shape of the s...
TL;DR: In this article, a simple evolutionary method for optimization of plates subject to constant weight, where design variable thicknesses are discrete, is presented, and an optimal design with minimum displacement or minimum strain energy is obtained by gradually shifting material from elements according to their sensitivity numbers.
Abstract: This paper presents a simple evolutionary method for optimization of plates subject to constant weight, where design variable thicknesses are discrete. Sensitivity numbers for sizing elements are derived using optimality criteria methods. An optimal design with minimum displacement or minimum strain energy is obtained by gradually shifting material from elements to the others according to their sensitivity numbers. A simple smoothing technique is additionally employed to suppress formation of checkerboard patterns. It is shown that the proposed method can directly deal with discrete design variables. Examples are provided to show the capacity of the proposed evolutionary method for structural optimization with discrete design variables.
TL;DR: In this paper, an evolutionary iterative process of finite element analysis is used to solve topology optimization and thickness distribution problems of thin shells subjected to thermal loading. But the authors focus on the problem of minimizing the number of stressed materials.
Abstract: The purpose of this paper is to show how the Evolutionary Structural Optimization (ESO) algorithm developed by Xie and Steven can be extended to optimal design problems of thin shells subjected to thermal loading. This extension simply incorporates an evolutionary iterative process of thermoelastic thin shell finite element analysis. During the evolution process, lowly stressed material is gradually eliminated from the structure. This paper presents a number of examples to demonstrate the capabilities of the ESO algorithm for solving topology optimization and thickness distribution problems of thermoelastic thin shells.
01 Jan 1999
TL;DR: In this paper, the topology optimization of strut-and-tie models in non-flexural reinforced concrete members by using the Evolutionary Structural Optimization (ESO) method for plane stress continuum structures with displacement constraints is investigated.
Abstract: This paper deals with the topology optimization of strut-and-tie models in non-flexural reinforced concrete members by using the Evolutionary Structural Optimization (ESO) method for plane stress continuum structures with displacement constraints. By means of systematically removing elements that have less contribution to the stiffness from the discritized concrete member, the actual load paths within the member are gradually characterized by the remaining elements. The optimal topology of the strut-and-tie model is determined from the performance index history based on the optimization criterion of minimizing the weight of the structure while the constrained displacement is within an acceptable limit. Two examples are provided to illustrate the effectiveness of the present procedure in automatically finding the actual load paths in a reinforced concrete deep beam with web openings and a corbel. It is demonstrated that the ESO method and the performance index are capable in generating reliable optimal strut-and-tie models that are supported by analytical solutions and experimental evidence, and can be used in practice especially in the design of complex structures where no previous experience is available.
01 Jan 1999
TL;DR: In this article, three performance indices developed by using the scaling design approach for assisting the selection of optimal topologies for the minimum-weight design of continuum structures subject to stress and displacement constraints are presented.
Abstract: This paper presents three performance indices developed by using the scaling design approach for assisting the selection of optimal topologies for the minimum-weight design of continuum structures subject to stress and displacement constraints. These performance indices are incorporated in the Evolutionary Structural Optimization (ESO) method to monitor the optimization process from which optimal topologies can be identified. Examples provided demonstrate that the proposed performance indices are effective indicators of material efficiency and can be used to compare the efficiency of structural topologies generated by different optimization methods.
TL;DR: Zhao et al. as discussed by the authors proposed a solution method for the simultaneous optimization of several different natural frequencies of a structure in general and a two dimensional structure in particular, which can be regarded as the further extension of the generalized evolutionary method.
Abstract: This paper presents a solution method, which can be regarded as the further extension of the generalized evolutionary method (Zhao et al. 1998a), for the simultaneous optimization of several different natural frequencies of a structure in general and a two dimensional structure in particular. The main function of the present method is to optimize the topology of a structure so as to simultaneously make several different natural frequencies of interest to be of the corresponding different desired values for the target structure. In order to develop the present method, the new contribution factor of an element is proposed to consider the contribution of an element to the gaps between the currently calculated values for the different natural frequencies of interest and their corresponding desired values in a weighted manner. Using this new contribution factor of an element, the most inefficiently used material can be detected and removed gradually from the design domain of a structure. Through applying the present method to optimize two and three different natural frequencies of a two dimensional structure, it has been demonstrated that it is possible and applicable to use the generalized evolutionary method for tackling the simultaneous optimization of several different natural frequencies of a structure in the structural design.
TL;DR: In this paper, the authors present some simple thinking on an age-old question that given a bridge of a certain span and loading, from the point of view of structural efficiency, where should the bridge deck be positioned? Generally, this decision is made for other reasons than structural efficiency such as aesthetics and the analyst is often presented with a fait accompli.
Abstract: This paper presents some simple thinking on an age-old question that given a bridge of a certain span and loading, from the point of view of the structural efficiency, where should the bridge deck be positioned? Generally, this decision is made for other reasons than structural efficiency such as aesthetics and the analyst is often presented with a fait accompli. Using the recently invented Evolutional Structural Optimisation (ESO) method, it is possible to demonstrate that having the deck at different vertical locations can lead to a very different mass and shape for each structural form resembling cable-stayed and cable-truss bridges. By monitoring a performance index which is the function of stresses and volume of discretised finite elements, the best optimised structure can be easily determined and the bridge deck positioning problem can be efficiently solved without resorting to any complex analysis procedures.
01 Jan 1999
TL;DR: In this article, the evolutionary structural optimization (ESO) method was used to develop optimal strut-and-tie models in structural concrete members by slowly removing a small number of elements with the least contribution to the stiffness from the discritized concrete member.
Abstract: The strut-and-tie modeling is a simple, unified, rational and safe approach for the design of structural concrete members. Conventional methods are not efficient in finding optimal strut-and-tie models in concrete members with complex geometry and loading conditions. In this paper, the Evolutionary Structural Optimization (ESO) method for continuum structures with displacement constraints is briefly outlined and used to develop optimal strut-and-tie models in structural concrete members. By treating prestressing forces as external loads, prestressed concrete members can be analyzed, optimized and dimensioned like reinforced concrete ones. By slowly removing a small number of elements with the least contribution to the stiffness from the discritized concrete member, the load-transferring mechanism in the member can be gradually chacreterized by the resulting topology. Numerical examples are presented to show the effectiveness of the proposed evolutionary material removal procedure in automatically generating optimal strut-and-tie models in reinforced and prestressed concrete members. Optimal strut-and-tie models obtained by using the ESO method are verified by the existing experimental evidence and analytical solutions.