Introduction to Macroscopic Optimal Design in the Mechanics of Composite Materials and Structures

Abstract

The main goal of building composite materials and structures is to provide appropriate a priori controlled physico-chemical properties. For this purpose, a strengthening is introduced that can bear loads higher than those borne by isotropic materials, improve creep resistance, etc. Composite materials can be designed in a different fashion to meet specific properties requirements.Nevertheless, it is necessary to be careful about the orientation, placement and sizes of different types of reinforcement. These issues should be solved by optimization, which, however, requires the construction of appropriate models. In the present paper we intend to discuss formulations of kinematic and constitutive relations and the possible application of homogenization methods. Then, 2D relations for multilayered composite plates and cylindrical shells are derived with the use of the Euler–Lagrange equations, through the application of the symbolic package Mathematica. The introduced form of the First-Ply-Failure criteria demonstrates the non-uniqueness in solutions and complications in searching for the global macroscopic optimal solutions. The information presented to readers is enriched by adding selected review papers, surveys and monographs in the area of composite structures.

Triangular Functionally Graded Porous Moderately Thick Plates—Deformations and Free Vibrations

“…Substituting the values of the coefficients in the general polynomial, we end up with trial function (14). The residual function R is determined as: R(x, y) = ∇ 4 w(x, y) + pM + ω 2 M for CPT or more complicated for FSDT and TSDT (16) For the residual function ( 16) the coefficients r i in Equation ( 14) are derived with the use of the Bubnov-Galerkin method.…”

“…Governing relations are derived with the method discussed by Muc [16]. For 3D structures, let us consider the following functional:…”

“…The results are almost identical for those derived for isotropic plates. For the residual function (16) the coefficients ri in Equation ( 14) are derived use of the Bubnov-Galerkin method.…”

Description of Mesoscale Static and Fatigue Analysis of 2D Woven Roving Plates with Convex Holes Subjected to Axial Tension

“…The detailed description of the above criteria is presented, e.g., in refs. [17,32]. Let us note that the Hill, Tsai-Wu, and Hashin criteria are used for the description of structures where both positive and negative values of stresses occur what is not observed in the analysed problem.…”

Irradiation Effects in Polymer Composites for Their Conversion into Hybrids

“…The discussion of radiation effects on polymer composites as the precursors of hybrids, the innovative materials, has opened a large door for the extended applications in several areas of the following activities: modeling [1,2], medicine [3,4], transport [5,6], energy [7,8], electronic devices [9,10], sensors [11,12], food packaging [13,14], building composite materials [15], water desalinization [16] and many others. The inclusion of hybrids through the composite category depends undoubtedly on the deep interpenetration and the specific association of the constituent phases [17]; an explanatory example for the capacity of ionizing radiation for the adjustment of polymer blends into hybrid structuration is the irradiation of chitosan/poly(vinyl alcohol) systems [18].…”