New Finite Element Theory

Author: Long Yiqiu
Publisher:
Publish Date: 2004-08-01
Features: This book can serve as a textbook and reference for graduate students and senior undergraduate students in fields such as mechanics, civil engineering, and mechanical engineering. It is also suitable for reference by teachers and scientific and technical personnel in related fields. This book is a monograph supported by the Huaxia Talent Fund and systematically presents the research achievements of Professor Long Yiqiu and his research team over more than 20 years in the field of novel finite elements. The book consists of 20 chapters. Except for the first and last chapters, the remaining 18 chapters are divided into three parts: Part 1 is the advancement of variational principles, introducing two achievements: partitioned variational principles and parameterized variational principles. These provide theoretical guidance for constructing novel finite elements. Part 2 is an introduction to the advancement of the finite element method, focusing on generalized coordinate elements. This opens up a new path between coordinate and non-coordinate elements, reasonably solving the convergence issue, allowing flexible selection of element construction schemes, and enriching and updating the subject content. Four additional achievements are introduced, including partitioned mixed methods, analytical test function methods, quadrilateral area coordinate methods, and spline function finite element methods, which serve as a perfect complement to the book. Combining the discussions of seven achievements, the book also introduces related new elements, totaling 108, which are compiled together for reference.