FEA Final Exam

FEA Final Exam A partial differential equation is the mathematical description of a ____________ physical process in which a dependent variable, u, is a function of _____________ independent variables, e.g, t, and x. In order to solve a PDE we need to know a set of __________. - Continuous, one or more, boundaries Assuming the principles of a standard discrete system: What is the dimension of an element stiffness matrix? - m X m m is the number of nodes in the element Assuming the principles of a standard discrete system: What is the dimension of the global stiffness matrix after assembly of the whole structure? - a X a a is the number of global nodes in the element and the summation of the local element Basic Workflow of FEA Model ______ Collect ______ Build _______ _______ to FE ______ Assign ______ Apply _______ Run analysis _____ of results _____ with calibration Analysis of results - Sketch Data Model(geometry) Discretize, mesh Materials and Properties BCs Sanity Check Iterate Complete the formula u=summation __*__ - Na=shape function Ua=approximate displacement vector Considering that we are given the partial differential equation for a physical problem. Why is it necessary for some cases to use numerical methods such as the finite element method? - Sometimes we can't get the exact solution of the known so we use the finite element method to approximate the solution. explain .dat file - data file- contains comments on job run and used to check errors explain .hm file - hypermesh file- where the model is created and meshed explain .inp file - input file- text file where material properties and BCs are inserted explain .odb file - output database results file- used in hyperview to view stresses and displacements Explain strong form - the strong form of the problem is described by a differential equation and boundary conditions. -d^2phi/dx^2 +Q(x)=0 Explain week form - the weak form of the problem is an integral function multiplied by an arbitray v and is set equal to zero. ∫v[−d2φdx2+Q(x)]dx=0 Galerkin method is the method of _________________. - Weighted Residuals Galerkin's method gives an approximate solution for our problem. What is the choice of our weighting function in Galerkin's method? - Wb=Nb