Equivalent strength conditions in calculations of elastic composite structures

2021 ◽  
Author(s):  
A. D. Matveev
Keyword(s):  
Composite Structures ◽  
Elastic Composite ◽  
Equivalent Strength

scholarly journals Method of Equivalent Strength Conditions in Composite Structures Evaluations

2021 ◽  
pp. 106-115
Author(s):  
A.D. Matveev
Keyword(s):  
Composite Structures ◽  
High Efficiency ◽  
Approximation Error ◽  
Regular Structure ◽  
Approximate Solutions ◽  
Discrete Models ◽  
The Finite Element Method ◽  
Elastic Bodies ◽  
Equivalent Strength ◽  
Computer Resources

It is important to know the error or the approximate solution when calculating the strength of elastic composite structures (bodies) using the finite element method (FEM). To construct a sequence of solutions according to the FEM is necessary for the evaluation of the approximation error. It involves the grinding procedure for discrete models. The implementation of the grinding procedure for basic models that take into account the inhomogeneous, micro-homogeneous structures of bodies within the microapproach requires ample computer resources. This paper proposes a method of equivalent strength conditions (MESC) to calculate the static strength of elastic bodies with a non-uniform, microuniform regular structure. The calculation of composite bodies strength according to the MESC is reduced to the calculation of isotropic homogeneous bodies strength using equivalent strength conditions. Adjusted equivalent strength conditions are used in the numerical implementation of the MESC. They take into account the error of the approximate solutions. If a set of loads is specified for a composite body, then generalized equivalent strength conditions are applied. The FEM-based calculation of composite bodies strength that follows the MESC using multigrid finite elements requires 103 ÷ 105 times less computer memory than a similar calculation using ground basic models of composite bodies. The provided example of strength calculation for a beam with an inhomogeneous regular fiber structure using the MESC shows its high efficiency. The main MESC implementation procedures are outlined.

scholarly journals Using PWE/FE Method to Calculate the Band Structures of the Semi-Infinite PCs: Periodic in x–y Plane and Finite in z -direction

2017 ◽  
Vol 42 (4) ◽  
pp. 735-742 ◽  
Author(s):  
Denghui Qian ◽  
Zhiyu Shi
Keyword(s):  
Finite Element ◽  
Band Structure ◽  
Plane Wave ◽  
Composite Structures ◽  
Phononic Crystal ◽  
Plane Wave Expansion ◽  
Fe Method ◽  
Band Structures ◽  
Wave Expansion ◽  
Elastic Composite

Abstract This paper introduces the concept of semi-infinite phononic crystal (PC) on account of the infinite periodicity in x-y plane and finiteness in z-direction. The plane wave expansion and finite element methods are coupled and formulized to calculate the band structures of the proposed periodic elastic composite structures based on the typical geometric properties. First, the coupled plane wave expansion and finite element (PWE/FE) method is applied to calculate the band structures of the Pb/rubber, steel/epoxy and steel/aluminum semi-infinite PCs with cylindrical scatters. Then, it is used to calculate the band structure of the Pb/rubber semi-infinite PC with cubic scatter. Last, the band structure of the rubbercoated Pb/epoxy three-component semi-infinite PC is calculated by the proposed method. Besides, all the results are compared with those calculated by the finite element (FE) method implemented by adopting COMSOL Multiphysics. Numerical results and further analysis demonstrate that the proposed PWE/FE method has strong applicability and high accuracy.

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