MAT 374 - Computational Continuum Mechanics

Course Objectives

1. To teach indices notation, vector and tensor algebra,
2. To teach the basic equations of deformation and motion of a continuum,
3. To provide the concepts of stress vector and stress tensor,
4. To obtain the equation of conservation of mass, momentum, angular momentum and energy,
5. To give constitutive equations of isotropic elastic solids,
6. To teach basic concepts of work, energy, virtual work, strain and kinetic energy.
7. To solve some basic problems of deformation of elastic beams, plane waves and plate vibration.
8. To model and solve continuum mechanics problems with MATLAB.

Course Description

Index and vector notation: scalar, vector and tensor concepts, summation convention. Deformation, length and angle changes, area and volume changes, strain invariants, principal axes. Simulation of deformation with MATLAB. Kinematics; velocity, acceleration, material derivative, kinematics of volume integral. Stress: stress vector and stress tensor, principal stresses. MATLAB applications related with stress. Compatibility conditions. Conversation laws: conservation of mass and balance of momentum, angular momentum and energy. Constitutive equation of isotropic elastic solid. Work and Energy: virtual work, strain and kinetic energy, Ritz energy method. Some MATLAB applications: Deformation of elastic beam, plane elastic waves, plate vibration.