What is the mathematical expression of the equation used in designing thinn plates?
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The mathematical expression used in designing thin plates varies depending on the specific problem being addressed. Different papers propose different mathematical models and equations for analyzing the behavior of thin plates. For example, Babouskos and Katsikadelis propose an optimization problem where the thickness variation law is established to maximize or minimize the fundamental frequency of the plate . Zholymbayev and Aniyarov develop a mathematical model of thin plate vibrations based on a system of differential equations for the computational case of point bonding . Oosterhuis introduces a parametric structural design tool that uses the membrane analogy and the "rain flow analogy" to analyze the structural behavior of thin plates loaded out-of-plane . Paris and de León formulate the problem of thin plates using two coupled Poisson equations expressed in integral form . Weisstein discusses the thin plate spline, which is the fundamental solution to the biharmonic equation and is used for interpolation and minimizing bending energy .
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| Papers (4) | Insight |
|---|---|
| The mathematical expression used in designing thin plates is U(r) = r^2lnr, where U(r) is the thin plate spline function and r is the distance from the center of the thin plate. | |
14 Citations | The mathematical expression of the equation used in designing thin plates is not provided in the paper. The paper discusses the formulation of the problem using two coupled Poisson equations and the evaluation of domain integrals using a collocation procedure. |
| The mathematical expression of the equation used in designing thin plates is not provided in the paper. | |
9 Citations | The mathematical expression for the equation used in designing thin plates is not provided in the paper. |
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