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

By Daryl L. Logan

A primary direction within the Finite aspect research offers an easy, simple method of the finite aspect approach that may be understood through either undergraduate and graduate scholars. It doesn't have the standard must haves (such as structural research) required by way of such a lot on hand texts during this zone. The ebook is written basically as a uncomplicated studying device for the undergraduate scholar in civil and mechanical engineering whose major curiosity is in pressure research and warmth move. The textual content is aimed toward those that are looking to practice the finite aspect strategy as a device to unravel functional actual difficulties. This revised fourth version comprises the addition of a big variety of new difficulties (including SI problems), an appendix for mechanical and thermal houses, and extra civil functions.

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

**Example text**

15), we obtain f^1x ¼ kðd^1x À d^2x Þ f^2x ¼ kðd^2x À d^1x Þ Now expressing Eqs. ( k Àk f^1x d^1x ¼ Àk k d^2x f^ 2x ð2:2:16Þ ð2:2:17Þ 34 d 2 Introduction to the Stiffness (Displacement) Method This relationship holds for the spring along the x^ axis. From our basic deﬁnition of a stiffness matrix and application of Eq. 1) to Eq. 17), we obtain ! k Àk k^ ¼ ð2:2:18Þ Àk k as the stiffness matrix for a linear spring element. Here k^ is called the local stiffness matrix for the element. We observe from Eq.

This reliable method of directly assembling individual element stiffness matrices to form the total structure stiffness matrix and the total set of stiffness equations is called the direct stiffness method. It is the most important step in the ﬁnite element method. For this simple example, it is easy to expand the element stiffness matrices and then superimpose them to arrive at the total stiffness matrix. However, for problems involving a large number of degrees of freedom, it will become tedious to expand each element stiffness matrix to the order of the total stiffness matrix.

1. K is symmetric, as is each of the element stiffness matrices. If you are familiar with structural mechanics, you will not ﬁnd this symmetry property surprising. It can be proved by using the reciprocal laws described in such References as [3] and [4]. 42 d 2 Introduction to the Stiffness (Displacement) Method 2. K is singular, and thus no inverse exists until sufﬁcient boundary conditions are imposed to remove the singularity and prevent rigid body motion. 3. The main diagonal terms of K are always positive.