# Finite Element Method for Membranes (2-D Solids)

• Maria Augusta Neto
• Ana Amaro
• Luis Roseiro
• José Cirne
• Rogério Leal
Chapter

## Abstract

The development of finite element equations for the stress analysis of two dimensional structures subjected to external loads that are applied within their 2-D geometrical plane will be presented in this chapter. The basic concepts, procedures and formulations can also be found in many existing textbooks [1–4]. The element developed is called membrane or 2D solid element. The finite element solution will solve only the selected mathematical model and that all assumptions in this model will be reflected in the predicted response. Thus, the choice of an appropriate mathematical model is crucial and completely determines the insight into the physical problem that we can obtain by this kind of analysis.

## Keywords

Shape Function Triangular Element Finite Element Solution Rectangular Element Rigid Body Mode
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

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© Springer International Publishing Switzerland 2015

## Authors and Affiliations

• Maria Augusta Neto
• 1
• Ana Amaro
• 1
• Luis Roseiro
• 2
• José Cirne
• 3
• Rogério Leal
• 3
1. 1.CEMUC - Centre for Mechanical EngineeringUniversity of CoimbraCoimbraPortugal
2. 2.Department of Mechanical EngineeringPolytechnic Institute of CoimbraCoimbraPortugal
3. 3.Department of Mechanical EngineeringUniversity of CoimbraCoimbraPortugal