Course content

A short review of matrix algebra.
Displacement and force methods in matrix notation: discretization, degrees of freedom, elements and system, stiffness and flexibility and virtual work (with emphasis on virtual displacements).
Element analysis: strong and weak form, assumed displacement shapes (functions), direct and indirect interpolation; element stiffness matrix and consistent load vector (including temperature); shear deformations, transformations, arbitrary cross sections and eccentricities.
System analysis: assembly of stiffness- and load matrices; boundary conditions and reaction forces; storage schemes and equation solving; static condensation and super elements.
Stability: differential equation for beam with axial force, Euler buckling and buckling length; geometric stiffness and solution of eigenvalue problem; buckling of plane frames.
Programs and their use; modelling and control.

Learning outcome

The course provides the matrix formulated methods of program aided static analysis of plane frame problems, including lineraized buckling. It also attempts to give an introduction to basic finite element analysis. Through the problem sets the student should gain sufficient insight and knowledge to become a qualified user of typical program tools for these types of analyses.

Learning methods and activities

Lectures and problem solving by means of hand calculations or computer. If there is a re-sit examination, the examination form may change from written to oral.

Compulsory assignments

• Exercises (hand calculations and PC)

Recommended previous knowledge

The subject requires TKT4122 Mechanics 2 and TMA4110/TMA4115 Calculus 3. TKT4124 Mechanics 3 is highly recommended.

Course materials

Lecture notes - to be specified at semester start.