Abstract
An analytical trapezoidal hierarchical element for the transverse vibration of Mindlin plates resting on two-parameter foundations is presented. Legendre orthogonal polynomials are used as enriching shape functions to avoid the shear-locking problem and to improve considerably the computational efficiency. Element matrices are integrated in closed form eliminating the numerical integration errors conventionally found. With the C0 continuity requirement, the element can be used to analyze any triangular and polygonal plates without difficulty, while the Kirchhoff p -version elements requiring C1 continuity are not as versatile. The computed natural frequencies for rectangular, skew, trapezoidal, triangular, annular, and polygonal plates on two-parameter foundations show that the convergence of the proposed element is very fast compared to the conventional linear finite elements with respect to the number of degrees of freedom used. Many numerical examples are given.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.