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)
We are going to consider the forces exerted on a material. These can be external or internal. External forces come in two flavors: body forces(given per unit mass or volume) and surface forces(given per unit area). If we cut a body of material in equilibrium under a set of external forces along a plane as shown in fig. 1. and consider one side of it we draw two conclusions: 1 the equilibrium provided by the loads from the side taken out is provided by a set of forces that are distributed among the material particles adjacent to
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
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
