Fahmy Mohamed Abdelsabour
Adham University College, Umm Al-Qura University, Makkah 28653, Saudi Arabia.
Faculty of Computers and Informatics, Suez Canal University, New Campus, Ismailia 41522, Egypt.
Polymers (Basel). 2022 Jul 16;14(14):2883. doi: 10.3390/polym14142883.
A new three-dimensional (3D) boundary element method (BEM) strategy was developed to solve fractional-order thermo-elastoplastic ultrasonic wave propagation problems based on the meshless moving least squares (MLS) method. The temperature problem domain was divided into a number of circular sub-domains. Each node was the center of the circular sub-domain surrounding it. The Laplace transform method was used to solve the temperature problem. A unit test function was used in the local weak-form formulation to generate the local boundary integral equations, and the inverse Laplace transformation method was used to find the transient temperature solutions. Then, the three-dimensional elastoplastic problems could be solved using the boundary element method (BEM). Initial stress and strain formulations are adopted, and their distributions are interpolated using boundary integral equations. The effects of the fractional-order parameter and anisotropy are investigated. The proposed method's validity and performance are demonstrated for a two-dimensional problem with excellent agreement with other experimental and numerical results.
基于无网格移动最小二乘法（MLS），开发了一种新的三维（3D）边界元法（BEM）策略，以解决分数阶热弹塑性超声波传播问题。温度问题域被划分为多个圆形子域。每个节点都是其周围圆形子域的中心。采用拉普拉斯变换法求解温度问题。在局部弱形式公式中使用单位测试函数来生成局部边界积分方程，并使用拉普拉斯逆变换法来求瞬态温度解。然后，可以使用边界元法（BEM）求解三维弹塑性问题。采用初始应力和应变公式，并使用边界积分方程对其分布进行插值。研究了分数阶参数和各向异性的影响。对于二维问题，该方法的有效性和性能得到了证明，与其他实验和数值结果具有很好的一致性。
