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
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-
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
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
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
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)
The state of stress at a point is completely determined when: 1. the stress vectors on three different planes are specified 2. the stress vectors on two different planes are speciale 3. the stress vectors one arbitrary plane is spec-
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)
The reaction on the left end is not exact because 1. The order of interpolation is too low, a higher order of interpolation would give the right reaction 2. The distributed load attributed to node one does not ke it into the solution
