User:Eml4500.f08.ateam.boggs.t/Lecture 4

Lecture 4 began with the announcement that the class would be using Wikiversity over Wikipedia. The discussion then quickly turned to topics related to Finite Element Analysis. The first topic was Trusses, Matrix Method found in chapter 4 of the book. To start this discussion Dr. Vu-Quoc drew for the class a Truss with two elastic bars. An elastic bar implies that the bar is deformable. In the diagram each beam is denoted with a number inside of a triangle, the element number. Each node is denoted with a global node number that is placed inside of a circle.

In the Global FBD each node number is placed inside of a circle, for the FBD of the individual bar elements the node number is distinguished by a local node number that is placed inside of a square. The number may or may not directly correspond to the Global node number that it is referencing. For example, with bar element one in figure 3 below the Global node number one is also the local node number one, but depending on the user's preference the local node number for global node one could be two and the local node number for two could be one. This is also apparent with bar element two in figure 4 below as Global node number two is local node number one and Global node number three is local node number two. For the forces shown in the FBD's of the two bar elements the correct nomenclature is a capital F with a superscript of the bar element number in parenthesis and a subscript degree of freedom. It is correct to start with the x-direction and then continue with the y-direction at each node when labeling the degree of freedom.



For bar elements one and two the displacements directly correspond to the forces and are to follow the same strategies listed above when labeling the diagram. Instead of a capital F being used, for the displacements a lower case d will occupy its space.

The next big step is determining the force displacement (FD) relationship.



Where F is the 2x1 column force matrix, K is the 2x2 stiffness matrix, and d is the 2x1 column displacement matrix.