弹性力学变分原理和有限元.pdf

弹性力学变分原理 和有限元 陈伟球（浙江大学交通工程研究所） 丁皓江（浙江大学岩土工程研究所） 2007年9月12 日 举例 变分学的历史 1662年法国学者Fermat提出了几何光学中的 最短时间原理科学史上第一个变分原理 1687年Newton 《自然哲学的数学原理》有在 “稀疏”介质中沿轴运动的转动物体所受的阻力 最小的形式问题力学中的第一个变分问题 1696年Johann Bernoulli提出著名的最速降线 问题（The Brachistochrone Problem ）变分 学的起源 1740年前后Euler研究等周问题奠定了变分 学的基础 The Bernoulli Family Nicolaus (1623-1708) Jacob Nicolaus Johann (1654-1705) (1662-1716) (1667-1748) Nicolaus (I) (1687-1759) Nicolaus (II) Daniel Johann (II) (1695-1726) (1700-1782) (1710-1790) Johann (III) Daniel (II) Jacob (II) (1744-1807) (1751-1834) (1759-1789) http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/ Swiss mathematician who was tutored by Johann Bernoulli. He worked at the Petersburg Academy and Berlin Academy of Science. He had a phenomenal memory, and once did a calculation in his head to settle an argument between students whose computations differed in the fiftieth decimal place. Euler lost sight in his right eye in 1735, and in his left eye in 1766. Nevertheless, aided by his phenomenal memory (and having practiced writing on a large slate when his sight was failing him), he continued to publish his re