Continuum mechanics studies the foundations of deformable body mechanics from a mathematical perspective. It also acts as a base upon which other applied areas such as solid mechanics and fluid mechanics are developed. This book discusses some important topics, which have come into prominence in the latter half of the twentieth century, such as material symmetry, frame-indifference and thermomechanics. The study begins with the necessary mathematical background in the form of an introduction to tensor analysis followed by a discussion on kinematics, which deals with purely geometrical notions such as strain and rate of deformation. Moving on to derivation of the governing equations, the book also presents applications in the areas of linear and nonlinear elasticity. In addition, the volume also provides a mathematical explanation to the axioms and laws of deformable body mechanics, and its various applications in the field of solid mechanics.

Continuum Mechanics : Foundations and Applications of Mechanics

Elastic buckling of a spherical shell, embedded in an elastic material and loaded by a far-field hydrostatic pressure is analysed using the energy method together with a Rayleigh—Ritz trial function. For simplicity, only axisymmetric deformations are considered and inextensional buckling is assumed. The strains within the structure that are pre-critical are assumed to be small for the linear theory to be applicable. An expression is derived relating the pressure load to the buckling mode number, from which the upper-bound critical load can be determined. It is found that the presence of the surrounding elastic medium increases the critical load of the shell and the corresponding buckling mode number. However, the results also show that the strain of the shell at the point of instability may not be small for typical values of material and geometric constants.

Buckling of a spherical shell embedded in an elastic medium loaded by a far-field hydrostatic pressure

Influence of stress interaction effects upon pore motion in solids

The problem of an infinite solid containing an arbitrary number of non-overlapping spherical cavities and inclusions with arbitrary sizes and locations is considered. The infinite solid and the spherical inclusions are made of different isotropic, linearly elastic materials. The spherical cavities are assumed to carry arbitrary tractions, and the spherical inclusions are assumed to be perfectly bonded to the infinite solid. The boundary and interfacial displacements and tractions are represented by truncated series of surface spherical harmonics. The problem involving multiple spherical features is replaced by a sequence of problems involving a single spherical feature via Schwarz's alternating method which accounts for the interactions in the course of an iterative process. Problems involving a single spherical feature are solved by employing the Papkovich–Neuber functions, and the interactions are evaluated by applying a least squares method. A robust scheme is introduced to control the total errors on the spherical boundaries and interfaces and to choose the number of terms in the series expansions. Several numerical examples are given to address the efficiency and the accuracy of the proposed method.

A boundary spectral method for elastostatic problems with multiple spherical cavities and inclusions

The paper presents an analytic solution for the stresses in a thick plate of infinite size containing a spherical inclusion or cavity eccentrically located between the surfaces. The plate is subject to a stress system symmetrical about the axis of revolution of the plate while the surfaces are stress-free. In the inclusion problem, the inclusion is assumed to be rigid and no slip occurs between the plate, and inclusion. In the cavity problem, the surface of cavity is assumed to be stress-free. The solutions of both problems are illustrated by numerical examples for the cases of all-round tension and circular bending.

Stresses in a thick plate containing an eccentric spherical inclusion or cavity Part I

On Symmetrical Strain in Solids of Revolution in Spherical Co-Ordinates

A nucleotide mutation in codon 75 of HLA‐C*04:01:01:01 results in a novel allele HLA‐C*04:279N.

Kuo-Liang Yang

Papers

On Symmetrical Strain in Solids of Revolution in Spherical Co-Ordinates

Discovery of a novel HLA‐C04 null allele, HLA‐C04:279N, in a Singaporean individual

Kuo-Liang Yang

Papers

On Symmetrical Strain in Solids of Revolution in Spherical Co-Ordinates

Discovery of a novel HLA‐C*04 null allele, HLA‐C*04:279N, in a Singaporean individual

Discovery of a novel HLA‐C04 null allele, HLA‐C04:279N, in a Singaporean individual