Chepurnenko Anton, Litvinov Stepan, Meskhi Besarion, Beskopylny Alexey
Strength of Materials Department, Faculty of Civil and Industrial Engineering, Don State Technical University, Rostov-on-Don 344000, Russia.
Department of Life Safety and Environmental Protection, Faculty of Life Safety and Environmental Engineering, Don State Technical University, Rostov-on-Don 344000, Russia.
Polymers (Basel). 2021 Jul 22;13(15):2408. doi: 10.3390/polym13152408.
A theoretical solution of the problem of thick-walled shell optimization by varying the mechanical characteristics of the material over the thickness of the structure is proposed, taking into account its rheological properties. The optimization technique is considered by the example of a cylindrical shell made of high-density polyethylene with hydroxyapatite subjected to internal pressure. Radial heterogeneity can be created by centrifugation during the curing of the polymer mixed with the additive. The nonlinear Maxwell-Gurevich equation is used as the law describing polymer creep. The relationship of the change in the additive content along with the radius r, at which the structure is equally stressed following the four classical criteria of fracture, is determined in an elastic formulation. Moreover, it is shown that a cylinder with equal stress at the beginning of the creep process ceases to be equally stressed during creep. Finally, an algorithm for defining the relationship of the additive mass content on coordinate r, at which the structure is equally stressed at the end of the creep process, is proposed. The developed algorithm, implemented in the MATLAB software, allows modeling both equally stressed and equally strength structures.
考虑到材料的流变特性，提出了一种通过改变结构厚度方向上材料的力学特性来解决厚壁壳优化问题的理论方案。以承受内压的含羟基磷灰石的高密度聚乙烯制成的圆柱壳为例，对优化技术进行了研究。在聚合物与添加剂混合固化过程中，可通过离心作用产生径向不均匀性。采用非线性麦克斯韦 - 古列维奇方程作为描述聚合物蠕变的定律。在弹性公式中确定了添加剂含量随半径r的变化关系，其中结构按照四种经典断裂准则等应力。此外，研究表明，在蠕变开始时等应力的圆柱体在蠕变过程中不再等应力。最后，提出了一种确定添加剂质量含量与坐标r之间关系的算法，在蠕变过程结束时结构在该坐标处等应力。在MATLAB软件中实现的所开发算法能够对等应力和等强度结构进行建模。
