What new element is Castigliano s Theorem introducing? 1. None, it's just a particular case of the PMPE 2. It's a totally different principle that allows to obtain solutions of elasticity problems with unprecedented accuracy and efficiency in- cluding relativistic effects
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)
Concept Question Which of the following statements is true 1. The PVD and the PMPE are equivalent 2. The PVD is more general 3. The PMPE applies to any kind of material 4. The stationary character of the potential en ergy is equivalent to the Pvd for elastic ma terials
which generalizes to the statement. This reduces the number of material constants from 81 to 54. In a similar fashion we can make use of the symmetry of the strain tensor This further reduces the number of material constants to 36. To further reduce the number of material constants consider the conclusion from the first law for elastic materials, equation
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
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
