Abstract
The use of mesh-based numerical methods for a 3D elasticity solution of thick plates involves high computational costs. This particularly limits parametric studies and material distribution design problems because they need a large number of independent simulations to evaluate the effects of material distribution and optimization. In this context, in the current work, the Proper Generalized Decomposition (PGD) technique is adopted to overcome this difficulty and solve the 3D elasticity problems in a high-dimensional parametric space. PGD is an a priori model order reduction technique that reduces the solution of 3D partial differential equations into a set of 1D ordinary differential equations, which can be solved easily. Moreover, PGD makes it possible to perform parametric solutions in a unified and efficient manner. In the present work, some examples of a parametric elasticity solution and material distribution design of multi-directional FGM composite thick plates are presented after some validation case studies to show the applicability of PGD in such problems.
Highlights
Shear deformations are important in the flexural behavior of thick plates, especially when they consist of composite or Functionally Graded Materials (FGM)
The main goal of the current work is to adopt an approach based on the Proper Generalized Decomposition (PGD) method that makes it possible to deal with 3D elasticity solutions of plate problems, parametric studies and material distribution design problems, while consuming small computational resources
When applying a separated representation of the field functions, the solution of a high-dimensional boundary value problem was reduced to a sequence of low dimensional (1D) sub-problems
Summary
Shear deformations are important in the flexural behavior of thick plates, especially when they consist of composite or Functionally Graded Materials (FGM). The main goal of the current work is to adopt an approach based on the PGD method that makes it possible to deal with 3D elasticity solutions of plate problems, parametric studies and material distribution design problems, while consuming small computational resources. This technique reduces computational costs considerably, and makes it possible to deal with problems in high-dimensional coordinate spaces Due to these advantages, the application of PGD has been quickly extended in a variety of problems in science and engineering. There are some analytical or semi-analytical solutions for three-dimensional elasticity plate problems These methods are successful in decreasing computational costs, they are limited in special boundary conditions, loading and material characteristics, and their application in general plate problems is restricted. Further examples are presented to show the applicability of the method in the material distribution design problems
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