The Sub-Region Variational Principles
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This chapter focuses on the developments of the variational principles which are usually considered as the theoretical basis for the finite element method. In this chapter, we will discuss the sub-region variational principles which are the results by the combination of the variational principles and the concept of sub-region interpolation. Following the introduction, the sub-region variational principles for various structural forms, i.e., 3D elastic body, thin plate, thick plate and shallow shell, are presented respectively. Finally, a sub-region mixed energy partial derivative theorem is also given.
Keywordsvariational principle sub-region variational principle sub-region mixed energy partial derivative theorem
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