Abstract
The objective of Chap. 1 is to introduce basic concepts that will be used for developing nonlinear finite element formulations in the following chapters. Depending on the level of the students or prerequisites for the course, this chapter or a part of it can be skipped. Basic concepts in this chapter include vector and tensor calculus in Sect.1.2, definition of stress and strain in Sect. 1.3, mechanics of continuous bodies in Sect. 1.4, and linear finite element formulation in Sect. 1.5. A MATLAB code for three-dimensional finite element analysis with solid elements will reinforce mathematical understanding.
The original version of this chapter was revised. An erratum to this chapter can be found at https://doi.org/10.1007/978-1-4419-1746-1_6
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- 1.
More specifically, D has major and minor symmetry.
- 2.
H m(Ω) is the Sobolev space of the order m, whose functions are continuously differentiable up to m − 1, and mth partial derivatives are integrable.
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Kim, NH. (2015). Preliminary Concepts. In: Introduction to Nonlinear Finite Element Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1746-1_1
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DOI: https://doi.org/10.1007/978-1-4419-1746-1_1
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