Continuum Mechanics. Mathematical Background. Syllabus Overview. Week 1 – Math Review (Chapter 2). Week 2 – Kinematics (Chapter 3). Week 3 – Stress & Conservation of mass, momenta and energy (Chapter 4 & 5). Week 4 – Constituative Equations & Linearized Elasticity (Chapter 6 & 7).
Week 1 – Math Review (Chapter 2).
Week 2 – Kinematics (Chapter 3).
Week 3 – Stress & Conservation of mass, momenta and energy (Chapter 4 & 5).
Week 4 – Constituative Equations & Linearized Elasticity (Chapter 6 & 7).
Week 7 – Fluid Mechanics, Heat Transfer & Viscoelasticity (Chapters 8 & 9).
Computer Project – 30%
Mid Term (Take Home) – 25%
Final (Take Home) – 30%
Homework - (15%)
Continuum mechanics forms the basis of CFD, Solid Mechanics, Thermal Profile Modeling.
1. Decide upon the goal of the problem and desired information;
2. Identify the geometry of the solid to be modeled;
3. Determine the loading applied to the solid;
4. Decide what physics must be included in the model;
5. Choose (and calibrate) a constitutive law that describes the behavior of the material;
6. Choose a method of analysis;
7. Solve the problem.
Where i is row number and j column number and the last term on the rhs is the determinant of the n-1 by n-1 matrix when the ith row and first column of D are removed
The Adjoint (also called adjunct) of a matrix is the transpose of the matrix obtained by replacing each element by its cofactor.
Properties of anisotropic solids can be represented by tensors. For the most part we will consider rank 1 (vectors) and rank 2 (matrices) tensors.
Matrix methods can be used to solve tensor (i.e. anisotropic continuum mechanics problems).
The trace of a tensor is the sum of its diagonal terms.
In general a tensor can be considered as an operator that can stretch and rotate space. It is possible to find components that have no rotation. These special components are eigenvalues and eigenvectors. How could this be useful?