Showing papers by "Grant P. Steven published in 2000"

Topology Optimization of Strut-and-Tie Models in Reinforced Concrete Structures Using an Evolutionary Procedure

Abstract: This paper presents a performance based evolutionary topology optimization method for automatically generating optimal strut-and-tie models in reinforced concrete structures with displacement constraints. In the proposed approach, the element virtual strain energy is calculated for element removal, while a performance index is used to monitor the evolutionary optimization process. By systematically removing elements that have the least contribution to the stiffness from the discretized concrete member, the load transfer mechanism in the member is 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 displacements are within acceptable limits. Several examples are provided to demonstrate the capability of the proposed method in finding the actual load transfer mechanism in concrete members. It is shown that the proposed optimization procedure can produce optimal strut-and-tie models that are supported by the existing analytical solutions and experimental evidence, and can be used in practice, especially in the design of complex reinforced concrete members where no previous experience is available.

Behavior of 3D orthogonal woven CFRP composites. Part I. Experimental investigation

Abstract: This paper presents an experimental investigation of the mechanical behavior and failure mechanism of three-dimensional (3D) orthogonal woven CFRP composite panels. The 3D composite panels are preformed using Torayca T-300 (3K) carbon fiber, and then infused with the Epicote 828 epoxy resin. The nominal proportions of the stuffer yarn, the filler yarn and the warp weaver (or z yarn) are 1:1.2:0.2, respectively, and the overall fiber volume fraction is 43%. The 3D fiber architectures are measured and visualized in a micrograph form. Quasi-static tensile coupon tests are carried out to measure the in-plane Young's modulus, Poisson's ratio, tensile failure strengths and failure strains in both stuffer and filler yarn directions. Test results reveal that the average Young's modulus in the filler yarn direction is higher than that in the stuffer yarn direction, and the average failure strain in the filler yarn direction is lower than that in the stuffer yarn direction. The average failure strength in the filler yarn direction is slightly higher than that in the stuffer yarn direction. The fracture surfaces are studied using the scanning electron microscope (SEM) and the failure mechanism are then discussed. It is noted by studying the fracture surface that the fracture surface is always perpendicular to the loading direction. The crack causes the z yarn/matrix interface to debond. Also, the fracture of specimen cut along the x- (or stuffer yarn) direction causes filler yarn/matrix interface to debond and stuffer yarn to break, and the fracture of specimen cut along the y- (or filler yarn) direction causes stuffer yarn/matrix interface to debond and filler yarn to break. The testing results are then used to validate the developed models in Parts II and III of these series papers. In Part II, simplified analytical and finite element models are proposed to predict the mechanical property and failure strengths for the 3D orthogonal woven CFRP composites. In Part III, a curved beam model resting on an elastic foundation is presented to predict the tensile strength in the filler direction, and then to investigate the effect of some geometrical parameters on the tensile failure strength in the filler yarn direction.

Behavior of 3D orthogonal woven CFRP composites. Part II. FEA and analytical modeling approaches

Abstract: In this paper, a 3D macro/micro finite element analysis (FEA) modeling approach and a 3D macro/micro analytical modeling approach are proposed for predicting the failure strengths of 3D orthogonal woven CFRP composites. These approaches include two different scale levels, macro- and micro-level. At the macro-level, a relatively coarse structural model is used to study the overall response of the structure. At the micro-level, the laminate block microstructure is modeled in detail for investigating the failure mechanisms of 3D orthogonal woven CFRP composites. The FEA and analytical models developed previously [Tan P, Tong L, Steven GP. Modeling approaches for 3D orthogonal woven composites, Journal of Reinforced Plastics and Composites, 1998:17;545–577] are employed to predict the mechanical properties of 3D orthogonal woven CFRP composites. All models presented in this paper are validated by comparing the relevant predictions with the experimental results, which were reported earlier in Part I of the paper [Tan P, Tong L, Steven GP. Behavior of 3D orthogonal woven CFRP composites. Part I. Experimental investigation, Composites, Part A: Applied Science and Manufacturing, 2000:31;259–71]. The comparison shows that there is a good agreement for the mechanical properties. An acceptable agreement exists for the failure strength in the x or stuffer yarn direction even though the FEA model gives a lower bound and the analytical model gives an upper bound. However, for the failure strength in the y or filler yarn direction, the difference between the predicted and experimental results is significant due to primarily ignoring of the waviness of filler yarn in the models. A curved beam model, which considers the waviness of the filler yarn, will be presented in Part III of the paper.

Optimal Topology Design of Bracing Systems for Multistory Steel Frames

Abstract: This paper presents a performance-based optimization method for optimal topology design of bracing systems for multistory steel building frameworks with overall stiffness constraint under multiple lateral loading conditions. Material removal criteria are derived by undertaking a sensitivity analysis on the mean compliance of a structure with respect to element removal. A performance index is proposed to evaluate the performance of resulting bracing systems in the optimization process. In the proposed method, unbraced frameworks are initially designed under strength constraints using commercial standard steel sections from databases. The optimal topology of a bracing system for the multistory steel building framework is then generated by gradually removing inefficient materials from a continuum design domain that is used to stiffen the framework until the performance of the bracing system is maximized. Two design examples are provided to illustrate the effectiveness of the performance-based design optimization method proposed for the conceptual layout design of lateral bracing systems for multistory steel building frameworks.

Evolutionary topology and shape design for general physical field problems

Abstract: As a practical tool for design engineers, evolutionary techniques for structural topology, shape and size optimisation have successfully resolved the whole range of structural problems from frames to 2D and 3D continuums with design criteria of stress, stiffness, frequency and buckling. In view of the generality of the finite element formulation using either a variational calculus or weighted residual approach, it is logical to extend its applications to other steady state field problems in mathematical physics governed by partial differential equations. The range of physical problems falling to this category includes heat conduction, incompressible fluid flow, elastic torsion, electrostatics and magnetostatics, etc. This paper discusses the general principles involved in setting up the adaptive evolutionary algorithms that have finite element techniques as the analysis engines. To avoid the complexity of classical solutions, the proposed method develops a simple outer loop procedure consisting of finite element analysis and design modifications. Illustrative examples are presented to demonstrate the capability in solving the above-mentioned physical field situations.

Structural topology design with multiple thermal criteria

Abstract: This paper shows how the evolutionary structural optimization (ESO) algorithm can be used to achieve a multiple criterion design for a structure in a thermal environment. The proposed thermal ESO procedure couples an evolutionary iterative process of a finite element heat conduction solution and a finite element thermoelastic solution. The overall efficiency of material usage is measured in terms of the combination of thermal stress levels and heat flux densities by using a combination strategy with weighting factors. The ESO method then works by eliminating from the structural domain under‐utilized material. In this paper, a practical design example of a printed circuit board substrate is presented to illustrate the capabilities of the ESO algorithm for thermal design optimization in multiple load environments.

Introduction of fixed grid in evolutionary structural optimisation

Abstract: Introduces a faster and improved structural optimisation method which combines fixed grid finite element analysis (FG FEA) and evolutionary structural optimisation (ESO). ESO optimises a structure by removing a few elements at every iteration. FG methods allow fast mesh generation, fast solution and fast re‐evaluation of the modified meshes. The implementation of FG into the ESO process eliminates the need for regenerating the mesh and a few arithmetic calculations replace the full regeneration of the stiffness matrix every time the structure is modified. This greatly reduces the solution time, and the examples presented in this paper demonstrate and validate the method.

A method for varying the number of cavities in an optimized topology using Evolutionary Structural Optimization

Abstract: In recent years, the Evolutionary Structural Optimization (ESO) method has been developed into an effective engineering design tool, allowing various structural constraints to be incorporated into the optimization process such as natural frequency, buckling, stiffness, stress, displacement and heat However, no attempts have been made to incorporate nonstructural constraints such as the number of cavities in the final topology and manufacturing constraints This paper introduces a modification of the ESO method named Intelligent Cavity Creation (ICC) by which the number of cavities can be controlled This method has the additional benefit of eliminating the formation of checkerboard patterns The proposed ICC algorithm is applied to several optimization problems to show its effectiveness It is also demonstrated that ICC produces more practical topologies

A buildup voltage distribution (BVD) algorithm for shape control of smart plate structures

Abstract: An intuitive approach for the determination of voltage distribution in the application to shape control of smart structures using piezoelectric actuators is presented here. The algorithm called the Buildup Voltage Distribution (BVD) is based on an iterative approach inspired by a combination of existing iterative techniques. The mathematical model of the smart structure is based on a High Order Displacement (HOD) field coupled with a Layerwise Linear electric potential. The current shape control work will make use of the Finite Element (FE) formulation based on the above mentioned mathematical model. The development of the BVD algorithm makes no linearity assumption between displacement and voltage and hence can be applied to non-linear mathematical models. The algorithm will then be compared with two well-known algorithms. In addition, a patch insensitivity index is defined to identify the most and least effective locations for piezoelectric actuators.

Static shape control of composite plates using a slope-displacement based algorithm

Abstract: An intuitive approach for the determination of voltage distribution in the application to shape control of smart structures using piezoelectric actuators is presented. This novel approach introduces slope as the fine-tuning criterion on top of the common displacement-based shape control. The algorithm, called the perturbation buildup voltage distribution is based on an iterative approach inspired by a previous algorithm on displacement control. This method aims to provide a means of targeting the desired shape of a structure with a higher-order criterion such as slope. A natural consequence of this method is the smoothing of the resultant structure. This effect will be illustrated by numerical examples. Iterative parameters are varied to investigate favorable choices of the parameters. Results show that the slopes of the structure can be improved, but at a tolerable expense of the displacement criteria. Another result of practical interest is the reduction of internal stresses compared to cases using pure displacement shape control.

Shape functions generation using Macsyma

Abstract: An algorithm for the generation of general shape functions is presented here. The algorithm is coded using the Macsyma program which has symbolic/algebraic manipulation capabilities. The current technique is based on the direct approach of calculating shape functions which is seldom used due to manual algebraic tediousness. Listing of the code is included in this paper as well as examples showing how it correctly generates some of the common shape functions with ease. Two examples of new shape functions were created for C2 elements. Hence, the more useful purpose of this algorithm is that it can be used to investigate the existence of new types of shape functions by making use of the power of symbolic computational software. Copyright © 2000 John Wiley & Sons, Ltd.