Solid Mechanics

An useful guide on Solid Mechanics

✴ Solid mechanics is the study of the deformation and motion of solid materials under the action of forces. It is one of the fundamental applied engineering sciences, in the sense that it is used to describe, explain and predict many of the physical phenomena around us.✴

► Solid mechanics is fundamental for civil, aerospace, nuclear, and mechanical engineering, for geology, and for many branches of physics such as materials science. It has specific applications in many other areas, such as understanding the anatomy of living beings, and the design of dental prostheses and surgical implants. One of the most common practical applications of solid mechanics is the Euler-Bernoulli beam equation. Solid mechanics extensively uses tensors to describe stresses, strains, and the relationship between them.✦

【Topics Covered in this App are Listed Below】

⇢ Importance of Personality

⇢ Normal Strain,

⇢ Stress-Strain Diagrams – Specimen under tension

⇢ Offset yield stress

⇢ Hooke’s Law

⇢ Elasticity, plasticity, and creep

⇢ Shear Stress,

⇢ Shear Strain,

⇢ Sign Conventions for Shear Stresses and Strains

⇢ The elongation or shortening ()

⇢ Stress on inclined plane

⇢ Strain Energy

⇢ Impact loading

⇢ State of Plane stress

⇢ Stresses on Inclined Sections

⇢ Principal Stresses and Maximum Shear Stresses

⇢ Mohr’s Circle

⇢ Hooke’s law for plane stress

⇢ Stresses in Beams

⇢ Pure bending

⇢ Normal Stresses in Beams (Linearly Elastic Materials)

⇢ Shear stresses in beams of rectangular cross section

⇢ Beams with axial loads

⇢ Composite beams

⇢ Deflection of Beams: Introduction

⇢ Differential equation of the deflection curve

⇢ Moment area method

⇢ Macaulay’s method

⇢ Introduction Columns and Struts

⇢ Buckling and stability

⇢ Differential Equation for Column Buckling

⇢ Columns with other support conditions

⇢ Rankine Gordon formula

⇢ Thin cylinders & spheres - Introduction & differences

⇢ Basic Equations in Mechanics

⇢ Classification of the Response of Materials

⇢ Solution to Boundary Value Problems

⇢ Algebra of fourth order tensors

⇢ Eigenvalues, eigenvectors of tensors

⇢ Integral theorems

⇢ Kinematics

⇢ Deformation Gradient

⇢ Displacement, velocity and acceleration

⇢ Strain Tensors

⇢ Homogeneous Motions

⇢ Uniaxial or equi-biaxial motion

⇢ Compatibility condition

⇢ Other stress measures

⇢ Balance Laws

⇢ Conservation of momentum

⇢ Conservation of angular momentum

⇢ Constitutive Relations

⇢ Restrictions on constitutive relation

⇢ Restrictions due to Material Symmetry

⇢ Material parameters

⇢ Boundary Value Problem: Formulation

⇢ Symmetrical bending

⇢ 2D Elasticity solution

⇢ Shear center

⇢ End Torsion of Prismatic Bars

⇢ Twisting of thick walled closed section

⇢ Thin rolled section

⇢ Twisting of hollow section

⇢ Thin walled tubes

⇢ Bending of Curved Beams

⇢ Curved cantilever beam under end load

⇢ Beam on Elastic Foundation