Modern Trends in Structural and Solid Mechanics 1

Statics and Stability

Noel Challamel, Julius Kaplunov, Izuru Takewaki, Noel Challamel, Julius Kaplunov, Izuru Takewaki

• Éditeur: Wiley-ISTE
• Année: 2021
• ISBN:
  9781119831877
• Édition: 1
• Sujet: Physical Sciences
• Sous-sujet: Mechanics

This book - comprised of three separate volumes - presents the recent developments and research discoveries in structural and solid mechanics; it is dedicated to Professor Isaac Elishakoff.

This first volume is devoted to the statics and stability of solid and structural members. Modern Trends in Structural and Solid Mechanics 1 has broad scope, covering topics such as: buckling of discrete systems (elastic chains, lattices with short and long range interactions, and discrete arches), buckling of continuous structural elements including beams, arches and plates, static investigation of composite plates, exact solutions of plate problems, elastic and inelastic buckling, dynamic buckling under impulsive loading, buckling and post-buckling investigations, buckling of conservative and non-conservative systems and buckling of micro and macro-systems.

This book is intended for graduate students and researchers in the field of theoretical and applied mechanics.

1
Static Deformations of Fiber-Reinforced Composite Laminates by the Least-Squares Method

Accurate solutions of the linear elasticity equations governing three-dimensional static deformations of fiber-reinforced composite laminates are needed to efficiently design them for structural applications, by considering failure modes in them. In this chapter, the governing equations are written as first-order partial differential equations for three displacements, three transverse stresses and three in-plane strains. The mixed formulation facilitates the satisfaction of continuity conditions at an interface between two adjacent plies. These nine equations are numerically solved by minimizing residuals in them and in the boundary conditions by using the least-squares method. The functional of the residuals is evaluated by expressing the unknown quantities as the product of complete polynomials of different orders in the three independent coordinates and using appropriate quadrature rules. Minimization of the functional, with respect to coefficients appearing in the polynomials for the solution variables, provides a system of simultaneous linear algebraic equations that are numerically solved. It is shown that polynomial functions of degree, at most, 8 in the in-plane coordinates and 3 in the thickness coordinate for each layer of a laminate, provide accurate solutions for stresses and displacements when compared with the analytical solutions of problems. Through-the-thickness stress distributions are found to agree very well with those found analytically. It provides an efficient numerical scheme for accurately finding stresses and displacements in a laminate.

1.1. Introduction

Composites are being increasingly used in transportation, aviation and defense industries because of their high specific strength and our ability to tailor their elastic moduli and ultimate strengths in desired directions and at critical locations in the structure. They are usually in the form of a laminate composed of...