文档介绍：Chapter12 Sheet bending
Elasticity
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第十二章薄板弯曲
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Chapter12 Sheet bending
Summarization
§ 12-1 Basic Hypothesis
§ 12-2 Basic Functions
§ 12-3 Internal Force of Cross Section
§ 12-4 Boundary Condition of Sheet
§ 12-5 Solution of Sheet Bending under Rectangular
Coordinate
§ 12-6 Axisymmetric Bending of Circular Sheet
§ 12-7 Solution of Displacement of Sheet by Calculus
of Variation
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第十二章薄板弯曲
概述
第一节基本假设
第二节基本方程
第三节横截面上的内力
第四节薄板的边界条件
第五节薄板弯曲的直角坐标求解
第六节圆形薄板的轴对称弯曲
第七节变分法求薄板的位移
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Sheet Bending
Summarization
Sheet is different from thick board。Generally,if the ratio of the thickness of the board and the minimal dimension of the board face satisfies:
We call the board sheet.
Choose the ordinate origin as a point of the middle plane, and axes of x and y in the middle plane, z perpendicular to it, which are shown in fig. .
We call the plane halves the thickness of the board
middle plane.
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薄板弯曲
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:
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。
我们把平分板厚度的平面称为中面。
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When sheet mon load, we always divide the load into ponents. 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.
Sheet Bending
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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。
薄板弯曲
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§ 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
The normal strain perpendicular to middle plane is very small, thus we can ignore it. Namely . From geometric equations, we have ,thus