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Showing 2 results for Analytical Solution
Optimized Design of Finite Isotropic Plates with Hexagonal Cutout by Metaheuristic Algorithms
M. H. Bayati Chaleshtari, M. Jafari,
Volume 37, Issue 1 (9-2018)
Abstract

This paper aims at optimizing the finite isotropic plates with the hexagonal cutout subjected to  plane loading using metaheuristic optimization algorithms. This research uses Differential Evolution Algorithm (DE) and Harmony Search Algorithm (HSA) from the evolutionary algorithm category, Big Bang- Big Crunch Algorithm (BB-BC) from the physics-based algorithm category, and Grey Wolf Optimizer Algorithm (GWO) and Particle Swarm Optimization (PSO) from the SI algorithm category; then the results of these algorithms are compared with each other. The results indicate that the grey wolf optimizer has the complete performance, short solution time and the ability to avoid local optimums. In the analysis of finite isotropic plate, the effective parameters on stress distribution around the  hexagonal cutouts are cutout bluntness, cutout orientation, plate’s aspect ratio, cutout size, and type of loading. In this study, with the assumption of plane stress conditions, the analytical solution of Muskhelishvili’s complex variable method and conformal mapping is utilized. The plate is considered to be finite (the proportion ratio of the  diameter of circle circumscribing to the longest plate side should be more than 0.2), isotropic, and linearly elastic. The finite element method has been used to check the accuracy of the  results. Numerical results are in a  good agreement with those of the present analytical solution. The results show that by selecting the aforementioned parameters properly, less amounts of stress could achieve around the cutout can lead  to an increase in the load-bearing capacity of the structure.


Analytical and Numerical Study on the Buckling of Homogeneous Beams Coated by a Functionally Graded Porous Layer with Different Boundary Conditions
H. Salehipour,
Volume 41, Issue 1 (9-2022)
Abstract
In this paper, static buckling of homogeneous beams coated by a functionally graded porous layer with different boundary conditions is investigated based on the Timoshenko beam theory. The principle of virtual work has been used to obtain the governing equations. Two different methods, namely analyticalsolution and numerical solution are used to solve the governing equations and extract the buckling force. The governing equations are coupled as a series of ordinary differential equations. In the analytical solution, these equations are first uncoupled using a series of mathematical operations, and are then solved. The obtained solution has a series of parameters and unknown constants. Using the boundary conditions at the boundaries of the beam, a homogeneous system of equations is extracted, from which the axial buckling force is obtained. In the numerical solution, the generalized differential quadrature method is used to solve the static equations. Finally, the numerical results are presented and the effects of various parameters such as thickness to beam length ratio, porous layer thickness, porosity parameter, etc. on the buckling of the beam are investigated. Comparison of the results obtained from the two analytical and numerical solution methods confirms the accuracy and validity of both methods.
 
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