英汉双语弹性力学9课件.pptVIP

习题9.1 有一根高为a 的等边三角形截面扭杆，坐标如图所示。三角形三条边AB，OA，OB的方程分别为： 试证应力函数 能满足一切条件，并求出最大剪应力及扭角。 解： 将 代入相容方程 得 即 o x y B A a Thereupon The wringed pole hasn’t hole, obviously satisfies the boundary conditions on profile. From the boundary condition at the end of the pole: We get Consequently 故 扭杆无孔洞， 显然满足侧面边界条件 ，由杆端部边界条件 得 从而得 The shear stresses For equilateral triangle, from the membrane assimilation, we know:the maximum shear stress exists at Namely The twisty angle per unit length is: 剪应力 对于等边三角形，由薄膜比拟法知，最大剪应力发生在 处，即 单位长度上的扭角 Exercise 9.2 consider a pole with equal section. Its twisty angle per unit length is K, the shear elasticity module is . A function , where are real constants, is a function under affirmance. Solve the question: what is the conditions must satisfy, then can be viewed as stress function of the torsion problems? Substitute into the equation, we get Solution: if the given function can be used for the stress function of the torsion problems, if must satisfy the equations of compatibility: . This is the condition need satisfying. 习题9.2 等截面杆单位长度上的扭转角为K ，剪切弹性模量为 ，若函数 ，其中 为实常量， 为待定函数。试问： 满足什么条件时， 可作为扭转问题的应力函数？ 答： 若题意所给函数能作为扭转问题的应力函数，则该函数必须满足相容方程 将 代入后得 此即为 需满足的条件。 最后得到解答 于是由 横截面上任意一点的合剪应力是 §9-3 Membrane Assimilation From the example of the last section, we know: for the simple equal section pole of elliptic, we just give the calculating expression of shear stress at the cross-section, we haven’t pointed out the position and direction of the maximum shear stress at the section; but for the poles with not too complex section such as rectangular and thin cliff, it is considerably difficult to solve its precise solution, let alone the relatively complex section pole. For this reason, we introduce the method of me