Mechanics 3

Principle of virtual work. Plastification, collapse analysis and plastic hinges. Strain energy. Virtual displacements and virtual forces. Unit load method. Static indeterminate systems. Deformations caused by temperature. Principle of stationary potential energy. Rayleigh-Ritz' method. Continuum mechanics/Theory of elasticity: Stresses and equilibrium, strains and compatibility, material law. Solution techniques. Classical thin-plate theory. Applications within 2D stress problems and plate problems.

Mechanics 3 is the first in solid mechanics linked to the field of study for the students who has chosen a specialization in structural engineering or industrial mechanics at MTBYGG, MTING and MTPROD. The course contains classical methods for calculation of structures together with an introduction to general elasticity theory. This course is a link between the basic courses Mechanics 1 and 2 and advanced courses that focus on numerical solution methods.

The course is a continuation of Mechanics 2, and gives a more general treatment of solid mechanics. The course consists of two parts. Part one covers virtual work and the principle of stationary potential energy applied on bars, beams and frames. Part two presents theory of elasticity, applied within plane problems. The course will give the necessary theoretical background on theory of elasticity and energy methods for TKT4180 and TKT4192.


Learning outcome:

Knowledge:
The candidate will get knowledge of:
- Central energy concepts: Strain energy and potential energy
- The difference between and determination of elastic and plastic moment capacity
- Energy principals: Virtual work and stationary potential energy
- Principle of virtual displacements and principle of virtual forces
- Background and use of unit-load method
- Rayleigh-Ritz’ method
- General definition of stress and strain in the theory of elasticity
- Definition of plane structures ("skiver") and plates and simple calculations of such components

Skills:
The candidate will be skilled on:
- Determine structural response with the principle of virtual work or stationary potential energy
- Determine plastic collapse load in a structure with the use of plastic hinges
- Use the unit-load method to determine deformations because of loads or temperature, or the response in statically indeterminate systems
- Use Rayleigh-Ritz’ method to find approximations for beams, plane structures ("skiver") and plates

General competence:
The candidate will get competence on:
- Background and different applications of work and energy principles in statics
- Basic three-dimensional elasticity theory
- Theory of thin plates

Lectures and mandatory exercises.