scholarly journals A new proof of the dual optimization problem and its application to the optimal material distribution of SiC/graphene composite

2020 ◽  
Vol 1 (1) ◽  
pp. 187-191
Author(s):  
Ji-Huan He ◽  
Keyword(s):  
Material Properties ◽  
Optimization Problem ◽  
Dual Problem ◽  
Direct Proof ◽  
Duality Gap ◽  
Material Distribution ◽  
Dual Problems ◽  
Graphene Composite ◽  
Stationary Conditions ◽  
Optimal Material

This paper presents a simple and direct proof of the dual optimization problem. The stationary conditions of the original and the dual problems are exactly equivalent, and the duality gap can be completely eliminated in the dual problem, where the maximal or minimal value is solved together with the stationary conditions of the dual problem and the original constraints. As an illustration, optimization of SiC/graphene composite is addressed with an objective of maximizing certain material properties under the constraint of a given strength.

Topological Optimization Technique for Free Vibration Problems

1995 ◽  
Vol 62 (1) ◽  
pp. 200-207 ◽  
Author(s):  
Zheng-Dong Ma ◽  
Noboru Kikuchi ◽  
Hsien-Chie Cheng ◽  
Ichiro Hagiwara
Keyword(s):  
Free Vibration ◽  
Optimization Algorithm ◽  
Optimization Problem ◽  
Optimization Technique ◽  
Topological Optimization ◽  
Material Distribution ◽  
Eigenvalue Optimization ◽  
Shift Parameter ◽  
Vibration Problems ◽  
Optimal Material

A topological optimization technique using the conception of OMD (Optimal Material Distribution) is presented for free vibration problems of a structure. A new objective function corresponding to multieigenvalue optimization is suggested for improving the solution of the eigenvalue optimization problem. An improved optimization algorithm is then applied to solve these problems, which is derived by the authors using a new convex generalized-linearization approach via a shift parameter which corresponds to the Lagrange multiplier and the use of the dual method. Finally, three example applications are given to substantiate the feasibility of the approaches presented in this paper.

Distribution Parameter Optimization of an FGM Pressure Vessel

2011 ◽  
Vol 320 ◽  
pp. 404-409
Author(s):  
Ze Wu Wang ◽  
Shu Juan Gao ◽  
Qian Zhang ◽  
Pei Qi Liu ◽  
Xiao Long Jiang
Keyword(s):  
Analytical Solution ◽  
Pressure Vessel ◽  
Material Properties ◽  
Optimization Design ◽  
Optimal Solution ◽  
Functionally Graded ◽  
Material Distribution ◽  
Optimization Scheme ◽  
Graded Material ◽  
Optimal Material

Functionally graded material (FGM) is well-known as one of the most promising materials in the 21stcentury, which has become the hot issue on its mechanical behavior and composition design. The optimization design of the material distribution properties for an FGM hollow vessel subjected to internal pressure were investigated in this paper. By constructing an exponentially function determining the material properties, the general analytical solution of the stresses of the FGM pressure vessel was given based on the Euler-Cauchy formula. And then, an optimization model for obtaining the optimal material distribution of FGM vessel was proposed coupling the general finite element (FE) code. The discrepancy between the analytical solution and the numerical solution was about 2%, which verified the reliability of the proposed models, and the optimization results also proved the feasibility of proposed optimization scheme because of arriving at the optimal solution in a few iterations. Results obtained would be helpful in designing an FGM pressure vessel.

Tailoring the Fundamental Frequency of Laminated Composite Panels Using Material Properties

2014 ◽  
Vol 709 ◽  
pp. 157-161
Author(s):  
Li Guo Zhang ◽  
Kang Yang ◽  
Wei Ping Zhao ◽  
Song Xiang
Keyword(s):  
Fundamental Frequency ◽  
Material Properties ◽  
Present Method ◽  
Optimization Problem ◽  
Laminated Composite ◽  
Composite Panels ◽  
Fundamental Frequencies ◽  
Laminated Panels ◽  
Frequency Optimization ◽  
Optimal Material

Optimization of material properties is performed to maximize the fundamental frequency of the laminated composite panels by means of the genetic algorithm. The global radial basis function collocation method is used to calculate the fundamental frequency of clamped laminated composite panels. In this paper, the objective function of optimization problem is the maximum fundamental frequency; optimization variables are material properties of laminated panels. The results for the optimal material properties and the maximum fundamental frequencies of the 2-layer plates are presented to verify the validity of present method.

On the Prediction of Extremal Material Properties and Optimal Material Distribution for Multiple Loading Conditions

1994 ◽  
Author(s):  
Martin P. Bendsøe ◽  
Alejandro R. Díaz ◽  
Robert Lipton ◽  
John E. Taylor
Keyword(s):  
Material Properties ◽  
Optimization Problem ◽  
Simultaneous Optimization ◽  
Elastic Continuum ◽  
Linear Elastic ◽  
Recent Developments ◽  
Multiple Loading ◽  
Optimal Material ◽  
The Cost ◽  
Structural Optimization Problem

Abstract This paper describes some recent developments that treats the simultaneous optimization of material and structure for minimum compliance. The basic idea is to represent the material properties for a linear elastic continuum in the most general form possible namely as the unrestricted set of elements of positive semi-definite constitutive tensors. The cost of resource is measured through certain invariants of the tensors, here the 2-norm or the trace of the tensors. The advantage of this general formulation is that analytical forms for the optimized material properties can be derived and that effective methods for computational solution can be devised for the resulting reduced structural optimization problem.

scholarly journals The Use of the Duality Principle to Solve Optimization Problems

2018 ◽  
Vol 6 (1) ◽  
pp. 33
Author(s):  
Rowland Jerry Okechukwu Ekeocha ◽  
Chukwunedum Uzor ◽  
Clement Anetor
Keyword(s):  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Linear Program ◽  
Duality Gap ◽  
Duality Principle ◽  
Primal Problem ◽  
Optimal Values ◽  
Primal And Dual Problems ◽  
Primal And Dual

<p><span>The duality principle provides that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. The solution to the dual problem provides a lower bound to the solution of the primal (minimization) problem. However the optimal values of the primal and dual problems need not be equal. Their difference is called the duality gap. For convex optimization problems, the duality gap is zero under a constraint qualification condition.<span>  </span>In other words given any linear program, there is another related linear program called the dual. In this paper, an understanding of the dual linear program will be developed. This understanding will give important insights into the algorithm and solution of optimization problem in linear programming. <span> </span>Thus the main concepts of duality will be explored by the solution of simple optimization problem.</span></p>

An Analytical Model to Predict Optimal Material Properties in the Context of Optimal Structural Design

1994 ◽  
Vol 61 (4) ◽  
pp. 930-937 ◽  
Author(s):  
M. P. Bendsoe ◽  
J. M. Guedes ◽  
R. B. Haber ◽  
P. Pedersen ◽  
J. E. Taylor
Keyword(s):  
Material Properties ◽  
Structural Design ◽  
Optimization Problem ◽  
Existence Of Solutions ◽  
Simultaneous Optimization ◽  
Elastic Continuum ◽  
Linear Elastic ◽  
Optimal Material ◽  
Structural Optimization Problem ◽  
Principal Strains

This paper deals with the simultaneous optimization of material and structure for minimum compliance. Material properties are represented in the most general form possible for a (locally) linear elastic continuum, namely the unrestricted set of elements of positive semi-definite constitutive tensors and cost measures based on certain invariants of the tensors. Analytical forms are derived for the optimized material properties. These results, which apply in general, indicate that the optimized material is orthotropic with the directions of orthotropy following the directions of principal strains. The analysis for optimization of the material leads to a reduced structural optimization problem, for which the existence of solutions can be shown and for which effective methods for computational solution can be devised.

Generative design and analysis of a double-wishbone suspension assembly: a methodology for developing constraint oriented solutions for optimum material distribution

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Aayush Bhat ◽  
Vyom Gupta ◽  
Savitoj Singh Aulakh ◽  
Renold S. Elsen
Keyword(s):  
Design Methodology ◽  
Manufacturing Industry ◽  
Optimization Technique ◽  
Design Solution ◽  
Material Distribution ◽  
Generative Design ◽  
Trade Off ◽  
Content Type ◽  
Life Study ◽  
Optimal Material

Purpose The purpose of this paper is to implement the generative design as an optimization technique to achieve a reasonable trade-off between weight and reliability for the control arm plate of a double-wishbone suspension assembly of a Formula Student race car. Design/methodology/approach The generative design methodology is applied to develop a low-weight design alternative to a standard control arm plate design. A static stress simulation and a fatigue life study are developed to assess the response of the plate against the loading criteria and to ensure that the plate sustains the theoretically determined number of loading cycles. Findings The approach implemented provides a justifiable outcome for a weight-factor of safety trade-off. In addition to optimal material distribution, the generative design methodology provides several design outcomes, for different materials and fabrication techniques. This enables the selection of the best possible outcome for several structural requirements. Research limitations/implications This technique can be used for applications with pre-defined constraints, such as packaging and loading, usually observed in load-bearing components developed in the automotive and aerospace sectors of the manufacturing industry. Practical implications Using this technique can provide an alternative design solution to long periods spent in the design phase, because of its ability to generate several possible outcomes in just a fraction of time. Originality/value The proposed research provides a means of developing optimized designs and provides techniques in which the design developed and chosen can be structurally analyzed.

scholarly journals Mixed E-duality for E-differentiable Vector Optimization Problems Under (Generalized) V-E-invexity

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Najeeb Abdulaleem
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Duality Theorems ◽  
Differentiable Vector

AbstractIn this paper, a class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. The so-called vector mixed E-dual problem is defined for the considered E-differentiable vector optimization problem with both inequality and equality constraints. Then, several mixed E-duality theorems are established under (generalized) V-E-invexity hypotheses.

Genesis of Ribbed Plate and Shells With Isotropic Density Dependent Material

1993 ◽  
Author(s):  
Hans P. Mlejnek
Keyword(s):  
Working Conditions ◽  
Isotropic Material ◽  
Material Model ◽  
Elastic Behaviour ◽  
Material Distribution ◽  
Isotropic Model ◽  
Material Density ◽  
Layer Structures ◽  
Optimal Material ◽  
Theoretical Considerations

Abstract An essential part in the genesis of structures or optimal material distribution is the relation between elastic behaviour and material density. This approach makes use of a isotropic material model, which leads to very simple working conditions. The isotropic model is directly formulated and utilized without employing homogenization based on an artificial microstructure. It is shown in theoretical considerations and demonstrated by examples, that this idea works also very easily with plate and shells, even for very general layer structures.

Sign in / Sign up

Export Citation Format

Share Document