Elastic and Thermoelastic Responses of Orthotropic Half-Planes.

Yuriy V Tokovyy,Dariusz M Perkowski,Sebastian Lubowicki,Anatoliy V Yasinskyy

doi:10.3390/ma15010297

Abstract

A unified approach is presented for constructing explicit solutions to the plane elasticity and thermoelasticity problems for orthotropic half-planes. The solutions are constructed in forms which decrease the distance from the loaded segments of the boundary for any feasible relationship between the elastic moduli of orthotropic materials. For the construction, the direct integration method was employed to reduce the formulated problems to a governing equation for a key function. In turn, the governing equation was reduced to an integral equation of the second kind, whose explicit analytical solution was constructed by using the resolvent-kernel algorithm.

Highlights

The design of engineering applications and advancement of material science are driven projection and implementation of new composite materials with averaged properties meeting specific requirements [1]
The efficiency in developing optimization algorithms and procedures for the inverse identification of effective material parameters for advanced composite materials are directly related to the solutions of problems in solid mechanics [7,8,9]
Consider numerical implementation of the proposed solution algorithm for several case studies of the orthotropic materials with properties presented in Table 1 for the case of plane stress adopted in expressions for elastic coefficients in (4)

Summary

Introduction

The design of engineering applications and advancement of material science are driven projection and implementation of new composite materials with averaged properties meeting specific requirements [1] These requirements are usually formulated through both empirical evidence and a priori analysis implemented by inverse and optimization algorithms [2,3,4]. In contrast to the isotropic case, the eigenvalues of such problems for anisotropic solids will no longer be defined uniquely but depend on the interrelation between the elastic moduli involved into the coefficients of characteristic equations [6,25] This affects the type and character of corresponding eigenfunctions and complicates them, ensuring their vanishing behavior at distant points. These features make it quite attractive for the identification, inverse, and optimization algorithms [29]

Formulation of the Problem

Reduction to Governing Equations

Solution of the Governing Equations

Numerical Example and Discussion

Conclusions