What do you think the eigenvectors of the element stiff- ness matrix represent? 1. a basis in which the stiffness matrix would be diago- nal (if rotated to that basis) 2. a set of nodal displacements for the element corre-
Concept Question Which of the following statements is correct? Uo=U for ALL elastic materials(1 Uo=OijEij-U0 ONLY for linear elastic materials Jo=-ijEii for a nonlinear elastic material Statements(1) and 3)
Which of the following statements is correct? 1. The PVD only applies to linear elastic materials 2. The PVD applies only to elastic materials, but they can be linear or non-linear 3. The PVD applies regardless of the constitutive behavior of the material
Unit #10- Principle of minimum potential energy and Castigliano's First Theorem Principle of minimum potential energy The principle of virtual displacements applies regardless of the constitutive law. Restrict attention to elastic materials(possibly nonlinear). Start from the Pvd
Why is the element stiffness matrix singular in a finite element formulation? 1. So that it can accomodate rigid element dis- placements without introducing spurious nodal 2 Because we made a mistake in the formula- tion the stiffness matrix should not be sin- g 3. Because we havent enforced any displace ment boundary conditions(it's a variational approach after all) Statement(1)
Constitutive Law(6 equations, O unknowns) C Bound dary conditions of two types Traction or natural boundary conditions: For tractions t imposed on the portion of the surface of the body aBt Displacement or essential boundary conditions: For displacement
For the potato-shaped body given in class to explain the concept of stress, the field of stress vectors t(n)=t(n)(x)on the plane of normal n given by its cartesian components(1,0, 0) known and its cartesian components are given by the expression