Fundamentals of the Finite Element Method
Fundamentals of the Finite Element Method
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DOI：
10.1007/978-981-10-8135-4_4
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发表时间：
2018-06
期刊：
影响因子：
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通讯作者：
Shenghong Chen
中科院分区：
文献类型：
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作者：
Shenghong Chen
本章概述了有限元法的原理、控制方程和基本算法。自20世纪60年代后期以来，有限元法一直是工程设计和分析中最通用、最强大的计算工具。详细阐述了采用正交多项式级数的“标准”和“分级”形状函数，并在此基础上详细阐述了渗透率、温度和变形等领域的算法。对水工建筑物中有关岩石EDZ、潜水面、混凝土水化热、库水温度、动力响应等问题的求解技术进行了论述。本章最后讨论了水工建筑物的安全标准。
This chapter summarizes the principles, governing equations, and basic algorithms related to the finite element method (FEM), which has been the most general and powerful computation tool in the engineering design and analysis since the later 1960s. The “standard” and “hierarchical” shape functions using orthogonal polynomial series are elucidated in details, based on which the algorithms with regard to the fields of permeability, temperature, and deformation are elaborated. The solution techniques particularly important for hydraulic structures related to the issues of rock EDZ, phreatic surface, concrete hydration heating, reservoir water temperature, dynamic response, are addressed. This chapter is closed with the discussion on the safety criteria of hydraulic structures.