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.