A First Course in the Finite Element Method by Daryl L. Logan
This article is about the book "A First Course in the Finite Element Method" by Daryl L. Logan, which is a textbook for undergraduate and graduate students who want to learn the basics of the finite element method (FEM). FEM is a numerical technique for solving problems involving partial differential equations that arise in engineering and science.
The book covers various topics related to FEM, such as the formulation of element stiffness matrices and load vectors, the assembly of global equations, the solution of linear and nonlinear systems, the post-processing of results, and the applications to different types of problems. The book also introduces the use of MATLAB for FEM programming and provides several examples and exercises for practice.
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The book has six editions, with the latest one published in 2016 by Cengage Learning. The book can be downloaded for free from the Internet Archive[^1^] or purchased from online stores. A solution manual for the book is also available from Civil MDC[^2^] or other sources.
One of the main advantages of FEM is that it allows for easier modeling of complex geometrical and irregular shapes. Because the designer is able to model both the interior and exterior, he or she can determine how critical factors might affect the entire structure and why failures might occur. FEM also offers adaptability, as it can handle different types of materials, boundary conditions, and loading scenarios.
Another advantage of FEM is that it provides accurate and reliable results, as it can capture the local effects and stress concentrations that might be missed by other methods. FEM also allows for the verification and validation of the models and solutions, as it can compare them with experimental data or analytical solutions. FEM also enables the optimization and improvement of the design, as it can perform parametric studies and sensitivity analyses.
A third advantage of FEM is that it reduces the cost and time of the design process, as it can eliminate or minimize the need for physical testing and prototyping. FEM also facilitates the communication and collaboration among different disciplines and stakeholders, as it can generate graphical and numerical outputs that can be easily shared and interpreted. FEM also supports the innovation and creativity of the design, as it can explore new ideas and possibilities that might not be feasible or practical otherwise.
However, FEM also has some disadvantages that need to be considered. One of the main disadvantages of FEM is that it requires a large amount of data as input for the mesh used in terms of nodal connectivity and other parameters depending on the problem. It also requires a digital computer and fairly extensive computational resources. It may require longer execution time compared with other methods, especially for large and complex problems.
Another disadvantage of FEM is that it obtains only approximate solutions, as it relies on the assumptions and simplifications made in the modeling process. FEM also has inherent errors, such as discretization error, round-off error, and convergence error, that affect the accuracy and reliability of the results. Moreover, mistakes by users can be fatal, as they can lead to erroneous or misleading solutions.
A third disadvantage of FEM is that it does not produce a general closed-form solution, which would permit one to examine system response to changes in various parameters. FEM also depends on the availability and quality of the software packages and literature that implement the method. FEM also requires a good understanding of the theory and principles behind the method, as well as the experience and judgment of the user.
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