Download A First Course in the Finite Element Method (4th Edition) by Daryl L. Logan PDF

By Daryl L. Logan

A primary path within the Finite point research offers an easy, simple method of the finite aspect strategy that may be understood by way of either undergraduate and graduate scholars. It doesn't have the standard necessities (such as structural research) required by way of so much on hand texts during this sector. The e-book is written basically as a simple studying instrument for the undergraduate pupil in civil and mechanical engineering whose major curiosity is in tension research and warmth move. The textual content is aimed toward those that are looking to practice the finite aspect procedure as a device to resolve functional actual difficulties. This revised fourth version comprises the addition of a giant variety of new difficulties (including SI problems), an appendix for mechanical and thermal homes, and extra civil purposes.

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Extra resources for A First Course in the Finite Element Method (4th Edition)

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K2n 7< d2 = 7 .. 7> .. > . > . 5> > > > ; : > dn . . Knn ð1:4:7Þ where now n is the structure total number of unknown nodal degrees of freedom. These equations can be solved for the ds by using an elimination method (such as Gauss’s method) or an iterative method (such as the Gauss–Seidel method). These two methods are discussed in Appendix B. The ds are called the primary unknowns, because they are the first quantities determined using the stiffness (or displacement) finite element method. Step 7 Solve for the Element Strains and Stresses For the structural stress-analysis problem, important secondary quantities of strain and stress (or moment and shear force) can be obtained because they can be directly expressed in terms of the displacements determined in step 6.

K2n 7< d2 = 7 .. 7> .. > . > . 5> > > > ; : > dn . . Knn ð1:4:7Þ where now n is the structure total number of unknown nodal degrees of freedom. These equations can be solved for the ds by using an elimination method (such as Gauss’s method) or an iterative method (such as the Gauss–Seidel method). These two methods are discussed in Appendix B. The ds are called the primary unknowns, because they are the first quantities determined using the stiffness (or displacement) finite element method. Step 7 Solve for the Element Strains and Stresses For the structural stress-analysis problem, important secondary quantities of strain and stress (or moment and shear force) can be obtained because they can be directly expressed in terms of the displacements determined in step 6.

This means the structural system is unstable. Without our specifying adequate kinematic constraints or support conditions, the structure will be free to move as a rigid body and not resist any applied loads. In general, the number of boundary conditions necessary to make [K] nonsingular is equal to the number of possible rigid body modes. Boundary conditions are of two general types. Homogeneous boundary conditions—the more common—occur at locations that are completely prevented from movement; nonhomogeneous boundary conditions occur where finite nonzero values of displacement are specified, such as the settlement of a support.

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