A new algorithm for shape parameter optimization in the multiquadric method for bending beam and elastic plane BVPs.

In this study, an enhancement to the Multiquadric Radial Basis Function (MQ-RBF) method is presented for solving Elasticity Boundary Value Problems (E-BVPs). MQ-RBF is utilized to reproduce the system of governing partial differential equations and boundary conditions. Also the inefficacies of some existing methods in determining the Optimal Shape Parameter (OSP) when solving E-BVPs are shown. Afterward, a new algorithm is introduced based on Teaching–Learning-Based Optimization (TLBO). In addition, the lower and upper bounds of the shape parameter and a new objective function were introduced for the TLBO algorithm. Using the algorithm, one OSP is obtained for both MQ-RBF functions in 2D problems, resulting in reduced computational cost. Its efficiency is evidenced by solving several examples. Moreover, its accuracy is demonstrated by comparing its outcomes to those of analytical methods. Unlike the 1D problems, the OSP is found to be a function of loading and material properties as well as the geometry in 2D problems. [ABSTRACT FROM AUTHOR]