scholarly journals A Discretization Method for Solving Optimization Problems in Structural Design

1982 ◽  
Vol 18 (8) ◽  
pp. 763-769
Author(s):  
Yasuo TSUKAMOTO ◽  
Yasuyuki SEGUCHI
Keyword(s):  
Structural Design ◽  
Optimization Problems ◽  
Discretization Method

Topology Optimization Considering Gravitational and Centrifugal Forces

2006 ◽  
Author(s):  
Bin Zheng ◽  
Hae Chang Gea
Keyword(s):  
Topology Optimization ◽  
Kinetic Energy ◽  
Structural Design ◽  
Gravitational Force ◽  
Body Force ◽  
Optimization Problems ◽  
Sensitivity Analyses ◽  
Centrifugal Forces ◽  
Gravitational Forces ◽  
Mean Compliance

In this paper, topology optimization problems with two types of body force are considered: gravitational force and centrifugal force. For structural design under both external and gravitational forces, a total mean compliance formulation is used to produce the stiffest structure. For rotational structural design with high angular velocity, one additional design criteria, kinetic energy, is included in the formulation. Sensitivity analyses of the total mean compliance and kinetic energy are derived. Finally, design examples are presented and compared to show the effects of body forces on the optimized results.

Study on Random Analysis Method and its Application to Structures

2011 ◽  
Vol 183-185 ◽  
pp. 734-738
Author(s):  
Lin Cong Zhou ◽  
Yi Feng Zheng ◽  
Jian Hui Qiu
Keyword(s):  
Structural Design ◽  
Concrete Beam ◽  
Sampling Method ◽  
Latin Hypercube Sampling ◽  
Structural Systems ◽  
Discretization Method ◽  
Random Response ◽  
Analysis Method ◽  
Homogeneous Random Field ◽  
Fiber Element

The evaluation of the reliability of structural systems is of extreme importance in structural design, mainly when the variables are random. A method is presented to efficiently assess the random response of stochastic structures. The article uses two-level sampling method to partial fiber element. First, the homogeneous random field of concrete and rebar can be created by modified Latin-hypercube sampling. Then section discretization method is adopted to assign fiber random variables of concrete section fiber. The algorithm is then used to analyze the random response of a concrete beam, and the result proves that the method is efficient.

On Structural Optimization

1983 ◽  
Vol 50 (4b) ◽  
pp. 1139-1151 ◽  
Author(s):  
N. Olhoff ◽  
J. E. Taylor
Keyword(s):  
Structural Optimization ◽  
Structural Design ◽  
Optimization Problems ◽  
Rapid Development ◽  
Mathematical Formulation ◽  
Future Research ◽  
Special Importance ◽  
Continuum Structures ◽  
Main Emphasis ◽  
Basic Concepts

This paper presents a survey of the field of optimal structural design, with the main emphasis laid on fundamental aspects. The basic concepts for structural optimization problems are outlined, and we discuss the mathematical formulation and the characteristic properties and features of such problems for both discrete and continuum structures. A picture of the present status of the field is given, and we present an assessment of areas that are currently of special importance and undergoing rapid development. Furthermore, we identify some types of problems that require particular care in their formulation, and we indicate issues for future research.

Parametric Optimization for Structural Design Problems

2019 ◽  
Author(s):  
Krupakaran Ravichandran ◽  
Nafiseh Masoudi ◽  
Georges M. Fadel ◽  
Margaret M. Wiecek
Keyword(s):  
Structural Design ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Nonlinear Constraint ◽  
Computational Performance ◽  
Design Variables ◽  
Input Parameters ◽  
Parametric Optimization Problem ◽  
Objective Function Values

Abstract Parametric Optimization is used to solve problems that have certain design variables as implicit functions of some independent input parameters. The optimal solutions and optimal objective function values are provided as functions of the input parameters for the entire parameter space of interest. Since exact solutions are available merely for parametric optimization problems that are linear or convex-quadratic, general non-convex non-linear problems require approximations. In the present work, we apply three parametric optimization algorithms to solve a case study of a benchmark structural design problem. The algorithms first approximate the nonlinear constraint(s) and then solve the optimization problem. The accuracy of their results and their computational performance are then compared to identify a suitable algorithm for structural design applications. Using the identified method, sizing optimization of a truss structure for varying load conditions such as a varying load direction is considered and solved as a parametric optimization problem to evaluate the performance of the identified algorithm. The results are also compared with non-parametric optimization to assess the accuracy of the solution and computational performance of the two methods.

Robust Structural Design Optimization Under Non-Probabilistic Uncertainties

2011 ◽  
Author(s):  
Jiantao Liu ◽  
Hae Chang Gea ◽  
Ping An Du
Keyword(s):  
Structural Optimization ◽  
Design Optimization ◽  
Structural Design ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Global Optimality ◽  
Worst Case ◽  
Probabilistic Uncertainty ◽  
Structural Design Optimization

Robust structural design optimization with non-probabilistic uncertainties is often formulated as a two-level optimization problem. The top level optimization problem is simply to minimize a specified objective function while the optimized solution at the second level solution is within bounds. The second level optimization problem is to find the worst case design under non-probabilistic uncertainty. Although the second level optimization problem is a non-convex problem, the global optimal solution must be assured in order to guarantee the solution robustness at the first level. In this paper, a new approach is proposed to solve the robust structural optimization problems with non-probabilistic uncertainties. The WCDO problems at the second level are solved directly by the monotonocity analysis and the global optimality is assured. Then, the robust structural optimization problem is reduced to a single level problem and can be easily solved by any gradient based method. To illustrate the proposed approach, truss examples with non-probabilistic uncertainties on stiffness and loading are presented.

Optimal Structural Design in the USSR

1989 ◽  
Vol 42 (2) ◽  
pp. 27-37 ◽  
Author(s):  
Mark I. Reitman
Keyword(s):  
Structural Optimization ◽  
Optimum Design ◽  
Structural Design ◽  
Optimization Problems ◽  
Moving Loads ◽  
Mathematical Methods ◽  
3D Structures ◽  
Optimal Structural Design ◽  
Academic Researchers ◽  
Rigid Frames

Studies in structural optimization in Russia began more than a century ago and initially satisfied the needs of railroad engineering. Later Soviet academic researchers and engineers considered the optimum design of compressed and twisted bars, beams, arches, rigid frames, plates, shells, and various 3D structures under single and multiple statical, dynamical, and moving loads. Some new formulations of the optimization problems have been introduced and solved using classical and new mathematical methods. Several hundred contributions are briefly covered with references to 50 bibliographical sources.

scholarly journals Global Optimization for Mixed–Discrete Structural Design

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1529
Author(s):  
Jung-Fa Tsai ◽  
Ming-Hua Lin ◽  
Duan-Yi Wen
Keyword(s):  
Structural Design ◽  
Design Problem ◽  
Optimization Problems ◽  
Global Optimum ◽  
Computational Time ◽  
Optimization Approach ◽  
Global Optimality ◽  
Discrete Variables ◽  
Beam Design ◽  
Continuous And Discrete Variables

Several structural design problems that involve continuous and discrete variables are very challenging because of the combinatorial and non-convex characteristics of the problems. Although the deterministic optimization approach theoretically guarantees to find the global optimum, it usually leads to a significant burden in computational time. This article studies the deterministic approach for globally solving mixed–discrete structural optimization problems. An improved method that symmetrically reduces the number of constraints for linearly expressing signomial terms with pure discrete variables is applied to significantly enhance the computational efficiency of obtaining the exact global optimum of the mixed–discrete structural design problem. Numerical experiments of solving the stepped cantilever beam design problem and the pressure vessel design problem are conducted to show the efficiency and effectiveness of the presented approach. Compared with existing methods, this study introduces fewer convex terms and constraints for transforming the mixed–discrete structural problem and uses much less computational time for solving the reformulated problem to global optimality.

Enabling the Extended Compact Genetic Algorithm for Real-Parameter Optimization by Using Adaptive Discretization

2010 ◽  
Vol 18 (2) ◽  
pp. 199-228 ◽  
Author(s):  
Ying-ping Chen ◽  
Chao-Hong Chen
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Economic Dispatch ◽  
Continuous Optimization ◽  
Memetic Algorithms ◽  
Discretization Method ◽  
Adaptive Discretization ◽  
Compact Genetic Algorithm ◽  
Economic Dispatch Problem ◽  
Continuous Optimization Problems

An adaptive discretization method, called split-on-demand (SoD), enables estimation of distribution algorithms (EDAs) for discrete variables to solve continuous optimization problems. SoD randomly splits a continuous interval if the number of search points within the interval exceeds a threshold, which is decreased at every iteration. After the split operation, the nonempty intervals are assigned integer codes, and the search points are discretized accordingly. As an example of using SoD with EDAs, the integration of SoD and the extended compact genetic algorithm (ECGA) is presented and numerically examined. In this integration, we adopt a local search mechanism as an optional component of our back end optimization engine. As a result, the proposed framework can be considered as a memetic algorithm, and SoD can potentially be applied to other memetic algorithms. The numerical experiments consist of two parts: (1) a set of benchmark functions on which ECGA with SoD and ECGA with two well-known discretization methods: the fixed-height histogram (FHH) and the fixed-width histogram (FWH) are compared; (2) a real-world application, the economic dispatch problem, on which ECGA with SoD is compared to other methods. The experimental results indicate that SoD is a better discretization method to work with ECGA. Moreover, ECGA with SoD works quite well on the economic dispatch problem and delivers solutions better than the best known results obtained by other methods in existence.

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