薄城曲 概述 薄板区别于厚板。通常情况下,板的厚度t与板面的最 小尺寸b的比值满足如下条件: 80100b(58 则称为薄板。 我们把平分板厚度的平 三==== 面称为中面。 将坐标原点取于中面 内的一点,x和y轴在中面 内,z垂直轴向下,如图 所示
6 概述 薄板区别于厚板。通常情况下，板的厚度t与板面的最 小尺寸b的比值满足如下条件: 8 1 ~ 5 1 100 1 ~ 80 1 ＜ ＜ b t 则称为薄板。 将坐标原点取于中面 内的一点,x和y轴在中面 内，z 垂直轴向下，如图 所示。 x y z o 我们把平分板厚度的平 面称为中面
When sheet accepts common load, we always divide the load into two components. One is transverse load, which is perpendicular to middle plane, one is longitudinal load, which acts in middle plane. For the latter, we assume its distributing is even along the thickness of the sheet, and treat it as the plane stress problem. In this chapter, we just discuss the stress, Strain and displacement when sheet is bent because of transverse load
7 When sheet accepts common load, we always divide the load into two components. One is transverse load, which is perpendicular to middle plane, one is longitudinal load, which acts in middle plane. For the latter, we assume its distributing is even along the thickness of the sheet, and treat it as the plane stress problem. In this chapter, we just discuss the stress、strain and displacement when sheet is bent because of transverse load
等遗 当薄板受有一般载荷时,总可以把每一个载荷分解 为两个分量,一个是垂直于中面的横向载荷,另一个是 作用于中面之内的纵向载荷。对于纵向载荷,可认为它 沿薄板厚度均匀分布,按平面应力问题进行计算。本章 只讨论由于横向载荷使薄板发生小挠度弯曲所引起的应 力、应变和位移
8 当薄板受有一般载荷时，总可以把每一个载荷分解 为两个分量，一个是垂直于中面的横向载荷，另一个是 作用于中面之内的纵向载荷。对于纵向载荷，可认为它 沿薄板厚度均匀分布，按平面应力问题进行计算。本章 只讨论由于横向载荷使薄板发生小挠度弯曲所引起的应 力、应变和位移
8 12-1 Basic Hypothesis For small bending problem of sheet, we generally adopt these assumptions (1) fixity of the board thickness The normal strain E perpendicular to middle plane is very small, thus we can ignore it. Namely .0 From geometric equations, we have =0, thus we get w=w(x, y) Namely: any normal which is perpendicular to middle plane has the same bending (2) fixity of normal of the middle plane
9 § 12－1 Basic Hypothesis For small bending problem of sheet, we generally adopt these assumptions: （1）fixity of the board thickness Namely: any normal which is perpendicular to middle plane has the same bending. （2）fixity of normal of the middle plane w= w(x, y) The normal strain perpendicular to middle plane is very small, thus we can ignore it. Namely . From geometric equations, we have ,thus we get: = 0 z = 0 z w z
薄城曲 §12-1基本假设 薄板小挠度弯曲问题,通常采用如下假设: (1)板厚不变假设 垂直于中面方向的正应变E很小,可以忽略不计。 即E=0,由几何方程aW=0,从而有: w=w(x,y) 即:在垂直于中面的任一条法线上,各点都具有相同的 挠度。 (2)中面法线保持不变假设 10
10 § 12－1 基本假设 薄板小挠度弯曲问题，通常采用如下假设： （1）板厚不变假设 W =W(x, y) 即：在垂直于中面的任一条法线上，各点都具有相同的 挠度。 （2）中面法线保持不变假设 垂直于中面方向的正应变 很小，可以忽略不计。 即 z = 0 ，由几何方程得 = 0 ，从而有： z W z