Performance-based optimization of structures: theory and applications

Performance-based Optimization of Structures introduces a method to bridge the gap between optimization theory and its practical applications to structural engineering. The performance-based optimization (PBO) method combines modern structural optimization theory with performance-based design concepts to produce a powerful technique for use in structural design. This book provides the latest PBO techniques for achieving optimal topologies and shapes of continuum structures with stress, displacement and mean compliance constraints. The emphasis is strongly placed on practical applications of automated PBO techniques to the strut-and-tie modeling of structural concrete, which includes reinforced and prestressed concrete structures. Basic concepts underlying the development of strut-and-tie models, design optimization procedure, and detailing of structural concrete are described in detail. The design optimization of lateral load resisting systems for multi-story steel and steel-concrete composite buildings is also presented. Numerous practical design examples are given which illustrate the nature of the load transfer mechanisms of structures

A posteriori modeling error estimates in the optimization of two-scale elastic composite materials

The a posteriori analysis of the discretization error and the modeling error is studied for a compliance cost functional in the context of the optimization of composite elastic materials and a two-scale linearized elasticity model. A mechanically simple, parametrized microscopic supporting structure is chosen and the parameters describing the structure are determined minimizing the compliance objective. An a posteriori error estimate is derived which includes the modeling error caused by the replacement of a nested laminate microstructure by this considerably simpler microstructure. Indeed, nested laminates are known to realize the minimal compliance and provide a benchmark for the quality of the microstructures. To estimate the local difference in the compliance functional the dual weighted residual approach is used. Different numerical experiments show that the resulting adaptive scheme leads to simple parametrized microscopic supporting structures that can compete with the optimal nested laminate construction. The derived a posteriori error indicators allow to verify that the suggested simplified microstructures achieve the optimal value of the compliance up to a few percent. Furthermore, it is shown how discretization error and modeling error can be balanced by choosing an optimal level of grid refinement. Our two scale results with a single scale microstructure can provide guidance towards the design of a producible macroscopic fine scale pattern

Variational approach to relaxed topological optimization: closed form solutions for structural problems in a sequential pseudo-time framework

The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a non-smoothed characteristic function field as a topological design variable, (c) the consistent derivation of a relaxed topological derivative whose determination is simple, general and efficient, (d) formulation of the overall increasing cost function topological sensitivity as a suitable optimality criterion, and (e) consideration of a pseudo-time framework for the problem solution, ruled by the problem constraint evolution. In this setting, it is shown that the optimization problem can be analytically solved in a variational framework, leading to, nonlinear, closed-form algebraic solutions for the characteristic function, which are then solved, in every time-step, via fixed point methods based on a pseudo-energy cutting algorithm combined with the exact fulfillment of the constraint, at every iteration of the non-linear algorithm, via a bisection method. The issue of the ill-posedness (mesh dependency) of the topological solution, is then easily solved via a Laplacian smoothing of that pseudo-energy. In the aforementioned context, a number of (3D) topological structural optimization benchmarks are solved, and the solutions obtained with the explored closed-form solution method, are analyzed, and compared, with their solution through an alternative level set method. Although the obtained results, in terms of the cost function and topology designs, are very similar in both methods, the associated computational cost is about five times smaller in the closed-form solution method this possibly being one of its advantages. Some comments, about the possible application of the method to other topological optimization problems, as well as envisaged modifications of the explored method to improve its performance close the workPeer ReviewedPostprint (author's final draft

A new hybrid method for size and topology optimization of truss structures using modified ALGA and QPGA

Modified Augmented Lagrangian Genetic Algorithm (ALGA) and Quadratic Penalty Function Genetic Algorithm (QPGA) optimization methods are proposed to obtain truss structures with minimum structural weight using both continuous and discrete design variables. To achieve robust solutions, Compressed Sparse Row (CSR) with reordering of Cholesky factorization and Moore Penrose Pseudoinverse are used in case of non-singular and singular stiffness matrix, respectively. The efficiency of the proposed nonlinear optimization methods is demonstrated on several practical examples. The results obtained from the Pratt truss bridge show that the optimum design solution using discrete parameters is 21% lighter than the traditional design with uniform cross sections. Similarly, the results obtained from the 57-bar planar tower truss indicate that the proposed design method using continuous and discrete design parameters can be up to 29% and 9% lighter than traditional design solutions, respectively. Through sensitivity analysis, it is shown that the proposed methodology is robust and leads to significant improvements in convergence rates, which should prove useful in large-scale applications

Designing manufacturable viscoelastic devices using a topology optimization approach within a truly-mixed fem framework

A new approach to topology optimization is presented that is based on the minimization of the input/output transfer function H∞norm. Additionally, by properly selecting input and output vector, the approach is recognized to minimize an entirely new definition of frequency-based dynamic compliance. The method is applied to viscoelastic systems in plane strain conditions that are investigated by using the Arnold-Winther finite-element resorting to a generalized solid phenomenological model. Preliminary indications on how to address the actual manufacturability of the optimal specimen are eventually outlined

An integrated approach to the optimum design of actively controlled composite wings

The importance of interactions among the various disciplines in airplane wing design has been recognized for quite some time. With the introduction of high gain, high authority control systems and the design of thin, flexible, lightweight composite wings, the integrated treatment of control systems, flight mechanics and dynamic aeroelasticity became a necessity. A research program is underway now aimed at extending structural synthesis concepts and methods to the integrated synthesis of lifting surfaces, spanning the disciplines of structures, aerodynamics and control for both analysis and design. Mathematical modeling techniques are carefully selected to be accurate enough for preliminary design purposes of the complicated, built-up lifting surfaces of real aircraft with their multiple design criteria and tight constraints. The presentation opens with some observations on the multidisciplinary nature of wing design. A brief review of some available state of the art practical wing optimization programs and a brief review of current research effort in the field serve to illuminate the motivation and support the direction taken in our research. The goals of this research effort are presented, followed by a description of the analysis and behavior sensitivity techniques used. The presentation concludes with a status report and some forecast of upcoming progress

Stress-Based Topology Optimization of Steel-Frame Structures Using Members with Standard Cross Sections: Gradient-Based Approach

This article presents a computationally efficient methodology for stress-based topology optimization of steel frame structures with cross-sectional properties that are mapped from I-beam sections of a design manual. To account for the natural variability of the data, this mapping is achieved via quantile regression to derive continuous relationships between cross-sectional area (the design variable) and other section properties. These relationships are used for deriving the gradient of structural performance, which allows using computationally efficient gradient-based optimization schemes. Three frame structures are designed using the proposed algorithm, the resulting designs are compared with traditional compliance-based topology optimization algorithms, and changes in the designs are discussed. A comparison of stress distribution within the designed structures verified the effectiveness of the proposed methodology