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The exhaustive list of topics in Solid Mechanics in which we provide Help with Homework Assignment and Help with Project is as follows:

  • Analysis of Stress:
    • Surface forces and traction/stress vector
    • Body forces and moments.
    • Components of stress matrix and its relation to stress vector.
    • Normal and shearing stresses on a plane
    • Stress transformations and stress tensor
    • Tensors.
    • Principal stresses and axes
    • Maximum shearing stress
    • Equilibrium equations
    • Boundary conditions.
  • Analysis of Deformation and Strain:
    • Deformation map
    • Displacement gradient
    • Straining of line element and strain components as measure of deformation.
    • Strain-displacement relations
    • Infinitesimal strain and linearization
    • Physical interpretation of normal and shear strain components.
    • Infinitesimal rotation vector and relative displacement
    • Straining of arbitrary line element
    • Strain transformation and strain tensor
    • Principal strains and axes.
    • Analogies with stress tensor
    • Volumetric strain and cubical dilation
    • Strain Compatibility equations.
  • Constitutive Relations, Boundary Value Problems:
    • Generalized Hooke's law
    • 3-D stress-strain relation for linear elastic Isotropic solid.
    • Compatibility equations in terms of stress
    • Types of boundary value problems (BVPs)
    • Displacement and stress formulations
    • Saint Venant's principle.
  • Two Dimensional Elasticity in Cartesian and Polar Coordinates:
    • Plane stress
    • Plane strain
    • Formulation of BVP using Airy stress function
    • Inverse and semi-inverse methods of solution.
    • Problems in rectangular coordinates
    • Polynomial solutions
    • Determination of displacements
    • Fourier series solutions.
    • Problems in polar coordinates
    • Transformation of field equations in polar coordinates
    • Axisymmetric problems
    • Non-axisymmetric problems
    • Stress concentrations
    • Use of symmetry in solving 2-D problems.
  • End Torsion of Bars (prismatic, general cross-section):
    • Review of torsion of circular sections
    • Formulation of BVP using Prandtl stress function and Saint Venant's semi-inverse method (Warping function method)
    • Membrane analogy.
    • Solutions for solid cross-section bars
    • Torsion of thin-walled open-section and closed-section (multi-celled) members.
    • Formulation for torsion of multi-celled thick-walled cross-sections
    • Finite difference method.
  • Bending of Beams (prismatic, general cross-section):
    • Preliminaries - sign conventions
    • Area moments of inertia and their transformation
    • Principal inertias.
    • Pure bending of beam with terminal couples
    • Bending of beam with end shear - BVP formulation
    • Examples
    • Shear center and its determination.
    • One-dimensional shear flow in open thin-walled beams and shear center problem solving.
  • Specific topics
  • Bending of Curved Beams:
    • Prismatic
    • Symmetric sectioned
    • Assumption
    • Derivation of basic results (kinematics, stresses)
    • Obtaining maximum stresses
    • Determining deflections using energy methods.
  • Beams on Elastic Foundation:
    • Basic problem of infinite beam with point load
    • various modifications of basic problem and application of superposition for solving them.