Abstract
The goal of this chapter is to demonstrate the finite element representation of two-dimensional elasticity problems by using rectangular and triangular elements. The minimum total potential energy principle is used to develop the equilibrium equations for an element of the deformable medium. Geometrically simple rectangular and triangular elements reveal the strength and shortcomings of the interpolations used in two-dimensional problems. Equations of equilibrium for a rectangular Q4 element and for a CST element are derived in detail. The potential drawbacks and limitations of the Q4 and CST elements are shown to be spurious shear strain, excessive stiffness, and shear locking. These defects can be eliminated for the most part by using higher order interpolations functions which result in increased number of nodes and degrees of freedom. Reasons for the improvements introduced by the higher order elements are discussed. The example given at the end of the chapter provides a top-level overview of using Q4 elements in analyzing a simple two-dimensional problem.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
