MECH 5130 Theory of Finite Element Method Scott Stapleton
MECH 5130 Theory of Finite Element Method Scott Stapleton
Homework 5: Load Vector
Complete (1), (2) and (3a) for pre-homework submission.
Create a bubble diagram of the functions needed for this homework. Make sure to find the most abstract tasks and create one bubble chart that works for both elements. Show the interdependency of the functions, using arrows connecting functions as shown below, where an incoming arrow should be labelled with the inputs for the function and an outgoing arrow labeled with the outputs. Indicate in RED the functions which will need to be customized for each element.
Function Name 1
Brief description of what function does or key equations
Function Name 2
920210-389605Brief description of what function does or key equations
Function Name 3
Function Name 4 Brief description of what
function does or key equations
11550057519887
Brief description of what function does or key equations
Write pseudo-code for each of the new functions in the bubble chart. Get to enough detail that you have worked out all the indices and dimensions of any arrays needed. Look up key functions needed and show that the arrays you give to the functions are in the right form.
19701932268784
3
4
3
486128710957125008943114562151762057736755931497114562160996017618194420255144529040328871444546For the 4-noded 2-D element shown below (E=70,000, =0.33, plane stress, = 1.3).
12
Derive the force vector for () = 0 + 1 in terms of the nodal locations, , the natural
2 + 3
coordinate and the thicknesses without performing the integral. How many integration points would you need to get an exact vector using Gaussian Quadrature?
Find the force vector using 0 = 4, 1 = 3, 2 = 5, 3 = 1, and the nodal coordinates above. (Hint: use this as a unit test)
4421259109917753282061072067For the 8-noded 2-D element shown below (E=70,000, =0.33, plane strain, = 1.3), find the force vector. State which degree of integration you used and why. State whether the integral solution is exact or not.
1898909363963215596442300523622102690752871357269075
4230103172709
84
4061338-9083811649384-16471667
6
5
7
6
5
123
