Mridula Sarkar

Intuitionistic Fuzzy Optimization of Truss Design: A Comparative Study

In this paper, we have developed an intuitionistic fuzzy optimization (IFO) approach considering non-linear membership and nonmembership function for optimizing the design of plane truss structure with single objectives subject to a specified set of constraints. In this optimum design formulation, the objective functions are the weight of the truss; the design variables are the cross-sections of the truss members; the constraints are the stresses in members. A classical truss optimization example is presented here in to demonstrate the efficiency of the Intuitionistic fuzzy optimization approach with non-linear membership function. We made a comparative study of linear and non-linear membership and non-membership function to see its impact on intuitionistic fuzzy optimization and to get to the depth of such optimization process. The test problem consists of a two-bar planar truss subjected to a single load condition. This single-objective structural optimization model is solved by intuitionistic fuzzy optimization approach with nonlinear membership and non-membership function. Numerical example is given to illustrate our approach. The result shows that the IFO approach is very efficient in finding the best discovered optimal solutions. Keywords— Intuitionistic fuzzy optimization, Nonlinear membership function, Non-linear nonmembership function, Structural design.

Optimization of Welded Beam Structure Using Neutrosophic Optimization Technique: A Comparative Study

This paper investigates neutrosophic optimization (NSO) approach to optimize the cost of welding of a welded steel beam, while the maximum shear stress in the weld group, maximum bending stress in the beam, maximum deflection at the tip and buckling load of the beam have been considered as flexible constraints. The problem of designing an optimal welded beam consists of dimensioning a welded steel beam such as height, length, depth, width of welded beam, so as to minimize its cost, subject to the constraints as stated above. The purpose of the present study firstly is to investigate the effect of truth, indeterminacy and falsity membership function in NSO in perspective of welded beam design in imprecise environment and secondly is to analyze the results obtained by different optimization methods like fuzzy, intuitionistic fuzzy and several deterministic methods so that the welding cost of the welded steel beam become most cost-effective. Specifically based on truth, indeterminacy and falsity membership function, a single-objective NSO algorithm has been developed to optimize the welding cost, subjected to a set of flexible constraints. It has been shown that NSO is an efficient method in finding out the optimum value in comparison with other iterative methods for nonlinear welded beam design in precise and imprecise environment. Numerical example is also given to demonstrate the efficiency of the proposed NSO approach.

Structural Design Optimization using Parameterized P-norm Based Geometric Programming Technique

In this paper we will make an approach to solve single objective structural model using parameterized p-norm based fuzzy Geometric Programming technique. A structural design model in fuzzy environment has been developed. Here pnorm based generalised triangular fuzzy number (GTFN) is considered as fuzzy parameter so that the decision maker can take advantage of no-exact parameter. Generalised triangular p-norm is discussed with their basic properties and some special cases. In this structural model formulation, the objective function is the weight of the truss; the design variables are the cross-sections of the truss members; the constraints are the stresses in members. A classical truss optimization example is presented here in to demonstrate the efficiency of our proposed optimization approach. The test problem includes a two-bar planar truss subjected to a single load condition. This approximation approach is used to solve this single-objective structural optimization model. The model is illustrated with numerical examples. Keywords— Generalized Triangular Fuzzy Number, p-norm, Geometric Programming, Single Objective Optimization, Structural Optimization.

Optimization of Structural Design by Fuzzy Geometric Programming Technique

In this paper we develop solution procedure of fuzzy geometric programming based on Warner’s approach for optimizing the design of plane truss structure with single objective subject to a specified constraint. In this optimum design formulation, the objective function is the weight of the truss; the design variables are the cross-sections of the truss members; the constraint is the stresses in member. A classical truss optimization example is presented here in to demonstrate the efficiency of this technique. The test problem includes a two-bar planar truss subjected to a single load condition. This single-objective structural optimization model is solved fuzzy geometric programming technique. Numerical example is given to illustrate our approach. Keyword:Two-bar Truss Design, GeometricProgramming,Fuzzy Geometric Programming, Warner’sApproach, Max-additive Operator.