By Peter I. Kattan
Later models. moreover, the CD-ROM features a whole strategies guide that comes with exact ideas to all of the difficulties within the booklet. If the reader doesn't desire to seek advice those options, then a quick checklist of solutions is equipped in published shape on the finish of the e-book. Iwouldliketothankmyfamilymembersfortheirhelpandcontinuedsupportwi- out which this ebook wouldn't have been attainable. i might additionally prefer to recognize assistance from the editior at Springer-Verlag (Dr. Thomas Ditzinger) for his counsel in bringing this booklet out in its current shape. eventually, i want to thank my brother, Nicola, for getting ready lots of the line drawings in either versions. during this version, i'm delivering e mail addresses for my readers to touch me (pkattan@tedata. web. jo and pkattan@lsu. edu). The previous e-mail tackle that seemed within the ?rst version used to be cancelled in 2004. December 2006 Peter I. Kattan PrefacetotheFirstEdition three this can be a e-book for those who love ?nite parts and MATLAB . we'll use the preferred computing device package deal MATLAB as a matrix calculator for doing ?nite aspect research. difficulties should be solved commonly utilizing MATLAB to hold out the tedious and long matrix calculations as well as a few guide manipulations in particular while employing the boundary stipulations. particularly the stairs of the ?nite aspect strategy are emphasised during this e-book. The reader won't ?nd ready-made MATLAB programsforuseasblackboxes. Insteadstep-by-stepsolutionsof?niteelementpr- lems are tested intimately utilizing MATLAB.
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Extra info for MATLAB Guide to Finite Elements: An Interactive Approach
Sample text
2) is solved by partitioning and Gaussian elimination. 3) where f is the 3 x 1 element force vector and u is the 3 x 1 element displacement vector, The element stresses are obtained by dividing the element forces by the crosssectional area A. 2 MATLAB Functions Used The four MATLAB functions used for the quadratic bar element are : QuadraticBarElementStiffness(E, A, L) - This function calculates the element stiffness matrix for each quadratic bar with modulus of elasticity E, cross-sectional area A, and length L.
QuadraticBarElementForces(k, u) - This function calculates the element force vector using the element stiffness matrix k and the element displacement vector u. It returns the 3 x 1 element force vector f . QuadraticBarElementStresses(k, u, A) - This function calculates the element stress vector using the element stiffness matrix k, the element displacement vector u and the cross-sectional area A. lt returns the 3 x 1 element stress vector sigma or s. The following is a listing of the MATLAB souree code for each function : function y = QuadraticBarElementStiffness(E,A ,L) %QuadraticBarElementStiffness This function returns the element % stiffness matrix for a quadratic bar % with modulus of elasticity E, % cross-sectional area A, and length L .
The global stiffness matrix for the structure, the displacement at node 2, the reactions at nodes 1 and 3, the stress in the bar, the force in the spring . A P. k ~ IC , 3 2 2m )1 Fig. 6. 1 Basic Equations The quadratic bar element is a one-dimensional finite element were the local and global coordinates coincide. It is characterized by quadratic shape functions. The quadratic bar element has modulus of elasticity E , cross-sectional area A, and length L. 1. The third node is at the middle of the element.