Finite Element Methods in Structural Analysis

Energy principles for establishing stiffness relationships for beam - , plane stress - , and plate bending problems. Global stiffness relationship achieved by element properties. Superelement and substructure techniques. Use of computer programs in finite element analysis. Examples of modelling of marine structures.

After completion of this subject the student understands the basis for finite element analysis of structures, is able to carry out finite element analysis with an existing computer program as well as critically assess the calculation results. At the end of the term the student is able to:

• Understand the energy principles that form the basis for the Finite Element Method.
• Understand how the stiffness relationships for a structure can be established.
• Understand what is meant by super-element and substructure techniques and what is the purpose of such techniques.
• Understand which criteria that need to be fulfilled to ensure that a Finite Element Method converges towards the exact solution when the mesh size is decreased.
• Understand which sources of error can influence the results of finite element analysis; including discretization errors and round off errors occuring during solving the resulting equation system.
• Establish the stiffness relationship for elements for trussworks, frames, thin plates with membrane or lateral loads; i.e., plane stress and plate bending problems based on energy principles and interpolation of the displacement fields.
• Explain how the stiffness relation for the (global) structure can be established by means of the element stiffness.
• Carry out a finite element analysis of a frame structure and a steel plated structure with membrane stresses by using a relevant computer program and critically assess the results of the analysis.

Lectures, exercises, including mandatory computer exercises. The subject will be lectured in English.