This is a strong-form method for two-dimensional thermal-mechanical problems.
The Chebyshev polynomial is used to obtain the derivatives of the variables with respect to intrinsic coordinates. By using the analytical expressions of the differentiation for the shape functions which are used for geometry mapping, the first- and second- derivatives of the variables with respect to global coordinates can be obtained directly. Based on the spectral derivative matrix and the element mapping technique, an accurate and efficient strong-form numerical method without any variational principles or energy principles can be obtained lastly for irregular domains.
A two-dimensional problem is given here from the paper"Galerkin free element method and its application in Fractural Mechanicals", example 1.
XIAOYE QIN (2020). Chebyshev element differential method for mechanical problem (https://www.mathworks.com/matlabcentral/fileexchange/82054-chebyshev-element-differential-method-for-mechanical-problem), MATLAB Central File Exchange. Retrieved .
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