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
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
16.21 Techniques of Structural Analysis and sig Spring 2003 Unit #1 In this course we are going to focus on energy and variational methods for structural analysis. To understand the overall approach we start by con- trasting it with the alternative vector mechanics approach
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
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
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