Composite material fracture complex variable method

Author: Yang Weiyang
Publisher:
Publish Date: 2005-03-01
Features: This book focuses on the application of complex function methods in the fracture theory of composite materials. It transforms the plane fracture problems of composite materials into boundary value problems of partial differential equations and employs complex function methods to derive analytical solutions for the stress, strain, displacement, bending moment, and torque at the crack tips of composite plates under Mode I, Mode II, Mode III, mixed-mode, pure bending, pure torsion, and bending-torsion loading. By considering the strain energy release rate as the limit of the average value of a real function, it obtains the calculation formulas for the strain energy release rates at crack tips of composite plates under various modes. It also converts the J-integral into a complex form—the real or imaginary part of a complex function integral—and proves the path independence of the J-integral at crack tips of composite plates. Most of the content in this book is the author's research achievements over the years. It can serve as a selective course textbook for senior undergraduate and graduate students in applied mathematics and engineering mechanics, and can also be used as a reference for teachers, engineers, and researchers in related fields.