Numerical Methods in Advanced Structural Mechanics

• Apply the Deformation/Stiffness Method to solve simple beam, truss and frame problems by hand calculations.
• Explain the assemblage of the global stiffness matrix and load vector for plane trusses and frames including accounting for boundary conditions.
• Explain the equivalence between the Deformation/Stiffness Method and the Finite Element Method.
• Use a mathematics program to analyze statically indeterminent truss and frame structures using the Deformation/Stiffness method.
• Account for the interpolation functions for simple bar, beam and plane elements.
• Account for the transformation of element stiffness matrices.
• Account for the solution of the global finite element system.
• Use a commercial finite element program to solve truss, frame and membrane problems.
• Perform convergence analysis for a finite element analyses.
• Analyze and evaluate deformations and stress distributions in a commercial finite element program.
• Critically evaluate the importance of the choice of element types, size and boundary conditions in finite element analysis.
• Perform finite element analysis of relevant applied problems within structural engineering.

The course concerns statically indeterminate elastic structures and analysis methods such as the Deformation/Stiffness Method and the Finite Element Method for plane structures, as well as application and training in the use of a commercial Finite Element Method (FEM) program.

The course has the following content:
– The Deformation/Stiffness method for trusses and frames.
– Distributed loads and equivalent nodal loads for bars and beams.
– Element stiffness matrix for plane beam elements, 2D and 3D beam elements.
– Transformation of elements in the plane.
– Boundary conditions and symmetry conditions.
– The Finite Element Method (FEM)
– Basic plane and solid continuum element types (formulations, advantages and disadvantages).
– Iso-parametric plane elements.
– Equivalent nodal loads for plane and solid continuum elements.
– Gaussian integration.
– Stress determination and mesh distribution.

• 36 – 49 (Mon 13-17)

41236/41951, knowledge of a mathematics software platform (Python, MatLab, Maple etc.) is recommended.

Lectures, group assignments and exercises.