Topology optimization of continuum structures with uncertain-but-bounded parameters for maximum non-probabilistic reliability of frequency requirement

2015 ◽  
Vol 23 (16) ◽  
pp. 2557-2566 ◽  
Author(s):  
Bin Xu ◽  
Lei Zhao ◽  
Yi Min Xie ◽  
Jiesheng Jiang
Keyword(s):  
Topology Optimization ◽  
Reliability Index ◽  
Optimization Problems ◽  
Mass Density ◽  
Limit State ◽  
Optimization Procedure ◽  
State Equation ◽  
Outer Loop ◽  
Continuum Structures ◽  
Beso Method

A method for the non-probabilistic reliability optimization on frequency of continuum structures with uncertain-but-bounded parameters is proposed. The objective function is to maximize the non-probabilistic reliability index of frequency requirement.The corresponding bi-level optimization model is built, where the constraints are applied on the material volume in the outer loop and the limit state equation in the inner loop. The non-probabilistic reliability index of frequency requirement is derived by the analytical method for the continuum structure with the uncertain elastic module and mass density. Further, the sensitivity of the non-probabilistic reliability index with respect to the design variables is analyzed. The topology optimization in the outer loop is performed by a bi-directional evolutionary structural optimization (BESO) method, where the numerical techniques and the optimization procedure of BESO method are presented. Numerical results show that the proposed BESO method is efficient, and convergent optimal solutions can be achieved for a variety of optimization problems on frequency non-probabilistic reliability of continuum structures.

A novel approach of reliability-based topology optimization for continuum structures under interval uncertainties

2019 ◽  
Vol 25 (9) ◽  
pp. 1455-1474 ◽  
Author(s):  
Lei Wang ◽  
Haijun Xia ◽  
Yaowen Yang ◽  
Yiru Cai ◽  
Zhiping Qiu
Keyword(s):  
Topology Optimization ◽  
Reliability Index ◽  
Large Scale ◽  
Optimization Problems ◽  
Uncertainty Propagation ◽  
Content Type ◽  
Continuum Structures ◽  
Novel Approach ◽  
Design Variables ◽  
Interval Uncertainties

Purpose The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval uncertainties of load and material parameters based on the technology of 3D printing or additive manufacturing. Design/methodology/approach First, the uncertainty quantification analysis is accomplished by interval Taylor extension to determine boundary rules of concerned displacement responses. Based on the interval interference theory, a novel reliability index, named as the optimization feature distance, is then introduced to construct non-probabilistic reliability constraints. To circumvent convergence difficulties in solving large-scale variable optimization problems, the gradient-based method of moving asymptotes is also used, in which the sensitivity expressions of the present reliability measurements with respect to design variables are deduced by combination of the adjoint vector scheme and interval mathematics. Findings The main findings of this paper should lie in that new non-probabilistic reliability index, i.e. the optimization feature distance which is defined and further incorporated in continuum topology optimization issues. Besides, a novel concurrent design strategy under consideration of macro-micro integration is presented by using the developed RBTO methodology. Originality/value Uncertainty propagation analysis based on the interval Taylor extension method is conducted. Novel reliability index of the optimization feature distance is defined. Expressions of the adjoint vectors between interval bounds of displacement responses and the relative density are deduced. New NRBTO method subjected to continuum structures is developed and further solved by MMA algorithms.

Topology Optimization of an Automotive Tailor-Welded Blank Door

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Guangyao Li ◽  
Fengxiang Xu ◽  
Xiaodong Huang ◽  
Guangyong Sun
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Lightweight Design ◽  
Optimization Procedure ◽  
Fe Model ◽  
Optimal Thickness ◽  
Evolutionary Structural Optimization ◽  
Wide Range ◽  
Beso Method ◽  
Tailor Welded Blank

Bidirectional evolutionary structural optimization (BESO) method has been successfully applied for a wide range of topology optimization problems. In this paper, the BESO method is further extended to the optimal design of an automotive tailor-welded blank (TWB) door with multiple thicknesses. Different from the traditional topology optimization for solid-void designs, topology optimization of the TWB door needs to identify the weld lines which joint sheets with different thicknesses. The finite element (FE) model of the automotive door assembly is established and verified by a series of stiffness experiments. Then, the proposed optimization procedure is applied to the optimization of the automotive TWB indoor panel for the optimal thickness layout and weld lines locations. Numerical results give guidelines for the lightweight design of TWB components to some extent.

Reliability Analysis of Fatigue Crack Growth with JC Method Based on Scientific Materials

2011 ◽  
Vol 63-64 ◽  
pp. 882-885 ◽  
Author(s):  
Xiao Li Zou
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Normal Distribution ◽  
Crack Growth ◽  
Reliability Index ◽  
Limit State ◽  
State Equation ◽  
Fatigue Reliability ◽  
Crack Propagation Process ◽  
Log Normal

Since the fatigue crack propagation process from initial size till final fracture is affected by lots of random factors, it is difficult to evaluate the fatigue reliability. Based on reliability theory, the first order second moment method ( JC method) is adopted to analyze and compute the fatigue reliability. To account for the uncertainties of material resistance, the parameters in the deterministic fatigue crack growth rate equation and material fracture toughness are taken as random variables with Normal distribution or Log-Normal distribution. Consequently, the limit state equation of fatigue crack growth is derived. The fatigue reliability index at any moment is calculated iteratively through JC method. As a computation example, the curve of fatigue crack growth reliability index with time is presented.

An Adaptive Continuation Method for Topology Optimization of Continuum Structures Considering Buckling Constraints

2017 ◽  
Vol 09 (07) ◽  
pp. 1750092 ◽  
Author(s):  
Xingjun Gao ◽  
Lijuan Li ◽  
Haitao Ma
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Continuation Method ◽  
Optimization Process ◽  
Continuum Structures ◽  
Design Evolution ◽  
Buckling Constraints ◽  
Load Factors ◽  
Structural Compliance ◽  
Parameter Values

This paper presents an adaptive continuation method for buckling topology optimization of continuum structures using the Solid Isotropic Material with Penalization (SIMP) model. For optimization problems of minimizing structural compliance subject to constraints on material volume and buckling load factors, it has been found that the conflict between the requirements for structural stiffness and stability may have an adverse impact on the performance of existing optimization algorithms. An automatic scheme for adjusting the penalization parameter is introduced to deal with this conflict and thus achieves better designs. Based on an investigation on the effect of the penalization parameter on design evolution during the optimization process, a rule is established to determine the appropriate penalization parameter values. Using this rule, an effective scheme is developed for determining the penalization parameter values such that the buckling constraints are appropriately considered throughout the optimization process. Numerical examples are presented to illustrate the effectiveness of the proposed method.

Matrix Algorithm for Reliability of Structure in Generalized Random Space

2012 ◽  
Vol 166-169 ◽  
pp. 1913-1916
Author(s):  
Xiao Jie Liu ◽  
Xiao Jing Li ◽  
Wei Hua Shi ◽  
Ya Chuan Kuang
Keyword(s):  
Reliability Index ◽  
Limit State ◽  
Random Variable ◽  
State Equation ◽  
Matrix Algorithm ◽  
Covariance Propagation ◽  
The Given

In this paper variance of preformance function is calculated according to law of covariance propagation and matrix algorithm is used to calculate reliability index of structures in generalized random space, which is applicable to independent and correlative random variable, linear or nonlinear limit state equation. The given example has shown that the proposed method is very simple and convenient.

Topology Optimization of Compliant Mechanisms Using Evolutionary Algorithm With Design Geometry Encoded as a Graph

2002 ◽  
Author(s):  
Shamim Akhtar ◽  
Kang Tai ◽  
Jitendra Prasad
Keyword(s):  
Topology Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Compliant Mechanism ◽  
Evolutionary Process ◽  
Optimization Procedure ◽  
Structural Topology ◽  
Mutation Operators ◽  
Design Variables ◽  
Straight Line

This paper describes an intuitive way of defining geometry design variables for solving structural topology optimization problems using an evolutionary algorithm (EA). The geometry representation scheme works by defining a skeleton which represents the underlying topology/connectivity of the continuum structure. As the effectiveness of any EA is highly dependent on the chromosome encoding of the design variables, the encoding used here is a graph which reflects this underlying topology so that the genetic crossover and mutation operators of the EA can recombine and preserve any desirable geometric characteristics through succeeding generations of the evolutionary process. The overall optimization procedure is applied to design a straight-line compliant mechanism : a large displacement flexural structure that generates a vertical straight line path at some point when given a horizontal straight line input displacement at another point.

scholarly journals Study on Structural Reliability of Prestressed Reinforced Concrete Beam Bridges Based on Full Probability Analysis

2021 ◽  
Vol 1210 (1) ◽  
pp. 012003
Author(s):  
Yubao Liu ◽  
Hanxiong Liu ◽  
Shouyi Sun
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Probability Distribution ◽  
Reliability Index ◽  
Limit State ◽  
State Equation ◽  
Distribution Model ◽  
State Equations ◽  
The Monte Carlo Method

Abstract A three dimensional(3D) finite element model is established for a prestressed concrete girder bridge, list the limit state equation and variable probability distribution model, obtain the failure probability and reliability index of the limit state equation based on the Monte-Carlo method, investigate the reliability index’s sensitivity to random variables for limit state equations of bridge bearing capacity. The specific method of the research on the structure reliability index calculation is to select a suitable way that can fit the research’s object among the center point method, the checking-point method, the Monte-Carlo method, the importance sampling method, and so on. Authors use finite element software ANSYS to build model and perform 3D force analysis. According to the results, authors can determine the bridges’ failure modes under the state of 3D stress. Then, authors can list the possible limit state equations related to Stiffness, strength, function, durability, and some character else. After determining the bridge’s structural limit state equation and the probability distribution model of the variables, determine the distribution function of each impact factor and its characteristic parameters through the site survey data and other related data surveys. Then, use the Monte-Carlo method for the calculation of bridge reliability index, obtain the failure probability and reliability index of each limit state equation, analyze the sensitivity of each variable to the reliability index under the ultimate state of the bridge’s bearing capacity. At last, authors give construction quality control plans and suggestions according to the data above.

An Efficient Method for Topology Optimization of Continuum Structures in the Presence of Uncertainty in Loading Direction

2016 ◽  
Vol 14 (05) ◽  
pp. 1750054 ◽  
Author(s):  
Jie Liu ◽  
Guilin Wen ◽  
Qixiang Qing ◽  
Yi Min Xie
Keyword(s):  
Topology Optimization ◽  
Efficient Method ◽  
Continuum Structures ◽  
Topology Optimization Problem ◽  
Multiple Load Cases ◽  
Evolutionary Structural Optimization ◽  
Interval Uncertainties ◽  
Beso Method ◽  
Multiple Load ◽  
Nonsymmetric Loading

This paper presents a simple yet efficient method for the topology optimization of continuum structures considering interval uncertainties in loading directions. Interval mathematics is employed to equivalently transform the uncertain topology optimization problem into a deterministic one with multiple load cases. An efficient soft-kill bi-directional evolutionary structural optimization (BESO) method is proposed to solve the problem, which only requires two finite element analyses per iteration for each external load with directional uncertainty regardless of the number of the multiple load cases. The presented algorithm leads to significant computational savings when compared with Monte Carlo-based optimization (MCBO) algorithms. A series of numerical examples including symmetric and nonsymmetric loading variations demonstrate the considerable improvement of computational efficiency of the proposed approach as well as the significance of including uncertainties in topology optimization when to design a structure. Optimums obtained from the proposed algorithm are verified by MCBO method.

scholarly journals Influence of Density-Based Topology Optimization Parameters on the Design of Periodic Cellular Materials

Materials ◽  
2019 ◽  
Vol 12 (22) ◽  
pp. 3736
Author(s):  
Hugo A. Alvarez ◽  
Habib R. Zambrano ◽  
Olavo M. Silva
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Optimization Procedure ◽  
Optimality Criteria ◽  
Cellular Materials ◽  
Initial Guess ◽  
Method Of Moving Asymptotes ◽  
Optimization Parameters ◽  
Common Technique ◽  
Moving Asymptotes

The density based topology optimization procedure represented by the SIMP (Solid isotropic material with penalization) method is the most common technique to solve material distribution optimization problems. It depends on several parameters for the solution, which in general are defined arbitrarily or based on the literature. In this work the influence of the optimization parameters applied to the design of periodic cellular materials were studied. Different filtering schemes, penalization factors, initial guesses, mesh sizes, and optimization solvers were tested. In the obtained results, it was observed that using the Method of Moving Asymptotes (MMA) can be achieved feasible convergent solutions for a large amount of parameters combinations, in comparison, to the global convergent method of moving asymptotes (GCMMA) and optimality criteria. The cases of studies showed that the most robust filtering schemes were the sensitivity average and Helmholtz partial differential equation based filter, compared to the Heaviside projection. The choice of the initial guess demonstrated to be a determining factor in the final topologies obtained.

Reliability Method and its Standard of the Composite Foundation Bearing Capacity

2012 ◽  
Vol 170-173 ◽  
pp. 144-147
Author(s):  
Xiao Yun Peng ◽  
Peng Ju Cui
Keyword(s):  
Bearing Capacity ◽  
Reliability Analysis ◽  
Reliability Index ◽  
Limit State ◽  
State Equation ◽  
Composite Foundation ◽  
Analysis Method ◽  
Cement Injection ◽  
Reliability Method ◽  
General Reliability

The general reliability analysis method of composite foundation bearing capacity was established with the example of cement injection pile, its limit state equation and the optimize method was presented, and the standard of reliability index was also proposed according to the corresponding demand of architectural structure. It indicate that the method is reasonable, convenient to calculation and can be popularized in the whole geotechnical engineering.

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