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线性弹性代数方程:基于MATLAB®的固体力学新力方法

English | 2024 | ISBN-10: 3031661737 | 229 pages| Epub PDF (True) | 19 MB

This book describes a second-generation force-based method emerging from a general formulation where the partial differential equations of elasticity are replaced by equivalent algebraic equations. These algebraic equations of linear elasticity can be used to solve statically indeterminate problems in reduced forms that define either the new second-generation force-based approach or a new displacement-based approach. The new force-based method can serve as the basis for teaching students at many technical levels how to solve equilibrium problems directly for the forces present. In elasticity courses, the derivation and use of the algebraic equations of linear elasticity can show how the difficulties of dealing with partial differential equations may be avoided by transforming those equations into algebraic equations with work-energy concepts. In a finite element course, a force-based finite element method can be described along with the traditional displacement-based approach to demonstrate how the two methods provide alternative ways for solving complex structural problems. Serving as a resource for including second-generation force-based methods in solid mechanics courses of an engineering curriculum, and as a robust learning resource, the book is ideal for instructors and for students, practicing engineers, and researchers.

英文|2024|ISBN-10:3031661737 |229页|Epub PDF(真)|19 MB 这本书描述了第二代基于力的方法,该方法从一个通用的公式中产生,其中弹性的偏微分方程被等效的代数方程所取代。这些线性弹性代数方程可用于求解简化形式的超静定问题,这些问题定义了新的第二代基于力的方法或新的基于位移的方法。新的基于力的方法可以作为在许多技术水平上教学生如何直接解决现有力的平衡问题的基础。在弹性课程中,线性弹性代数方程的推导和使用可以展示如何通过将偏微分方程转化为具有功能概念的代数方程来避免处理偏微分方程的困难。在有限元课程中,可以描述基于力的有限元方法以及传统的基于位移的方法,以演示这两种方法如何为解决复杂的结构问题提供替代方法。作为将第二代基于力的方法纳入工程课程固体力学课程的资源,以及作为强大的学习资源,这本书非常适合教师、学生、执业工程师和研究人员。
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