Applied Strength and Elasticity

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Department of Mechanics and Materials

Synopsis:

3D elasticity equations. Plane strain. Plane stress. Axial symmetry.

Coordinate transformation. Derivation of the equations of 2D elasticity. Airy stress function, principles of solution of 2D elasticity.

Plates. Kirchhoff's theory of thin plates. Mindlin's theory of thick plates.

Plate equation - numerical methods of solution. Solution by the finite difference method.

Shells. Rotationally symmetric shells. Membrane and bending theory of shells.

Nature of failure of materials and failure criteria.

Plasticity - introduction to mathematical theory of finite deformations. Tensor calculus.

Plasticity criteria, notation, incremental theory of plasticity.

Numerical methods of solution. Direct stiffness method. Solution of beam structures.

Numerical methods - overview. Variational principles in mechanics and dynamics.

Finite element method. Principle of the method, principles of spatial and time discretization, convergence of the method.

Types of FEM elements, overview. Stiffness matrix and element mass matrix, derivation.

Non-linear problems and methods of their solution. Principles of iterative methods.

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The course is a part of the following study plans: