## MATLAB Guide to Finite Elements: An Interactive Approach by Peter I. Kattan

By Peter I. Kattan

Later types. additionally, the CD-ROM encompasses a entire recommendations guide that comes with targeted strategies to the entire difficulties within the e-book. If the reader doesn't desire to seek advice those suggestions, then a quick checklist of solutions is supplied in revealed shape on the finish of the booklet. Iwouldliketothankmyfamilymembersfortheirhelpandcontinuedsupportwi- out which this booklet should not have been attainable. i'd additionally prefer to recognize assistance from the editior at Springer-Verlag (Dr. Thomas Ditzinger) for his suggestions in bringing this publication out in its current shape. ultimately, i want to thank my brother, Nicola, for getting ready many of the line drawings in either versions. during this version, i'm offering e-mail addresses for my readers to touch me (pkattan@tedata. internet. jo and pkattan@lsu. edu). The outdated electronic mail deal with that seemed within the ?rst variation used to be cancelled in 2004. December 2006 Peter I. Kattan PrefacetotheFirstEdition three it is a publication for those that 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 may be solved generally utilizing MATLAB to hold out the tedious and long matrix calculations as well as a few guide manipulations specially while utilising the boundary stipulations. particularly the stairs of the ?nite aspect procedure are emphasised during this ebook. The reader won't ?nd ready-made MATLAB programsforuseasblackboxes. Insteadstep-by-stepsolutionsof?niteelementpr- lems are tested intimately utilizing MATLAB.

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**Example text**

This is performed as follows in which we obtain the same results as above. 3 with E = 210 GPaandP = 18kN. 012 m 2 , respectively. Use linear bar elements to determine the displacement at the free end ofthe bar. 36 3. The Linear Bar Element p ------------------------ ---------~ X 3m Fig. 3. 2 Solution: Use the six steps outlined in Chapter 1 to solve this problem using the linear bar element. Step 1 - Discretizing the Domain: We will use five linear bar elements in this problem. 4. 2). 2 shows the element connectivity for this example.

0020 34 » 3. 0000 Thus the reactions at nodes land 3 are forces of 500 kN (directed to the left) and 510 kN (directed to the right), respectively. It is clear that force equilibrium is satisfied. Next we set up the element nodal displacement veetors UI and U2, then we calculate the element force veetors hand 12 by making calls to the MATLAB function LinearBarElementForces. Finally, we divide each element force by the cross-sectional area of the element to obtain the element stresses. 7 X 105 kN/m 2 (or 170 MPa, tensile).

2 MATLAB Functions Used 45 where U is the global nodal displacement vector and F is the global nodal force vector. At this step the boundary conditions are applied manually to the veetors U and F. 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.