Numerical methods of mechanics and dynamics

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Department of Mechanics and Materials

Synopsis:

Direct stiffness method. Application to truss structures. Tension/compression beam. Solution of truss structures. Variational formulation of tesion/compression beam.

Variational formulation of beam loaded in bending. Beam with shear effects (Timoshenko). Beam on elastic foundation (Timoshenko-Winkler). Beam loaded with M+N+T combination.

Isoparametric elements. Natural coordinates.

Isoparametric elements. Triangular and quadrilateral elements. Linear and quadratic elements T3 and T6, Q4 and Q8. Plane stress, plane strain.

Plane deformation, plane strain. Elements for plane problems.

Plane strain, plane strain. Derivation of element stiffness matrix.

Spatial elements. Summary of 2D and 3D elasticity in FEM. Use of symbolic algebra tools.

Linear dynamics and FEM. Hamilton's variational principle. Consistent and diagonal mass matrices. Solutions for natural shapes and natural frequencies solution.

Direct time integration of equations of motion. Implicit and explicit methods. Newmark's method.

Numerical integration. Solution of nonlinear problems.

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