Mathematical Modeling and Numerical Optimization of Composite Structures

Abstract

This chapter is devoted to modeling the properties of composite materials and structures. Mathematical relations describing the nonlinear elastic three-point bending of isotropic and reinforced beams with account of different strength and stiffness behavior in tension and compression are obtained. An algorithm for numerical solution of corresponding boundary-value problems is proposed and implemented. Results of numerical modeling were compared to acquired data for polymer matrix and structural carbon fiber reinforced plastics. A computational technology for analysis and optimization of composite pressure vessels was developed and presented.

Classification of Textile Polymer Composites: Recent Trends and Challenges

“…Figure 3 shows a typical problem-solving method under machine learning algorithms validated for numerous types of fiber reinforced polymer composites including CFRP, glass fiber reinforced polymer composites (GFRP), basalt fiber reinforced polymer composites (BFRP) and aramid fiber reinforced polymer composites (AFRP). Gonzalez introduced different mathematical models to detect nonlinear flexural deformation of CFRP based on stiffness level in compression and polymer matrices under different strength [101]. The study further presented modeling of different properties of fiber reinforced composite beams [102].…”

“…Gonzalez introduced different mathematical models to detect nonlinear flexural deformation of CFRP based on stiffness level in compression and polymer matrices under different strength [ 101 ]. The study further presented modeling of different properties of fiber reinforced composite beams [ 102 ].…”

Метод Асимптотического Расщепления В Динамических Задачах Пространственной Теории Упругости

“…График (2) показывает относительную погрешность для первых трех асимптотических приближений. Точность решения для всех трех приближений растет с уменьшением параметра ε. Так как для последовательности асимптотических приближений верна формула (20), то для ускорения сходимости асимптотического решения целесообразно применить операцию, заключающуюся в усреднении предыдущего и текущего асимптотических приближений. Тогда для второго и третьего усредненных асимптотических приближений справедливы формулы…”

On the Selection of a Composite Material for Two-Wheeler Foot Bracket Failure Prevention through Simulation and Mathematical Modeling

“…Golushko [15], discussed the varied strength and stiffness behaviour of materials under tension and compression, as illustrated by a three-point bending example. The addition of reinforcement particles such as Silicon Carbide (SiC), Titanium Carbide (TiC), Zinc (Zn), and Graphite (Gr) to metal matrix composites improved their characteristics, according to Sivagami et al [16] research.…”