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
The finite element method In FEMi we derale finite element equations fro PVD swe- SWe and obtained: K0=R:=4…n waere n:number of element nodal p Ue: elenent nodal displace ents
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
How can the paradox with the spring be plained? In other words, which of the following statements is true 1. Equilibrium can be derived from the equiv alence of the external and the internal work 2. Equilibrium is an artifact of our imagina- tion
Strain energy and potential energy of a beam brec sedans hoMe the neutra xxis remain So Figure 1: Kinematic assumptions for a beam Kinematic assumptions for a beam: From the figure: AA'=u3(a1) Assume small deflections: B B\,BB\=3+ duy