文档介绍：Chapter 3 Two-dimensional
Problems in Rectangular Coordinates
Elasticity
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第三章平面问题的直角坐标解答
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Chapter 3 Two-dimensional
Problem in Rectangular Coordinates
Two-dimensional Problems in Rectangular Coordinates
§3-1 Solution by Polynomials
§3-2 Determination of Displacements
§3-3 Bending of a Simply Supported
Beam by Uniform Load
§3-4 Loading of a Wedge by Gravity and
Hydraulic Pressure
§3-6 Bending of a Simply Supported
Beam by Arbitrary Lateral Load
§3-5 Solution by Series
Exercises
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第三章平面问题的直角坐标解答
平面问题的直角坐标解答
§3-1 多项式解答
§3-2 位移分量的求出
§3-3 简支梁受均布载荷
§3-4 楔形体受重力和液体压力
§3-5 级数式解答
§3-6 简支梁受任意横向载荷
习题课
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Stress Function in the form of a Polynomial of
the First Degree
§3-1 Solution by Polynomials
The ponents:
The Stress Boundary Condition:
Conclusion:(1)The linear stress function is corresponding to the state of no surface force and no stress.(2)There’s no effect to the stress to add a linear function to any stress function of two-dimensional problem.
Stress Function in the form of a Polynomial of
the Second Degree
Two-dimensional Problems in Rectangular Coordinates
。
to ,the ponents
0
,
2
,
0
=
=
=
=
yx
xy
y
x
a
t
t
s
s
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一、应力函数取一次多项式
§3-1 多项式解答
平面问题的直角坐标解答
应力分量:
应力边界条件:
结论:(1)线性应力函数对应于无面力、无应力的状态。
(2)把任何平面问题的应力函数加上一个线性函数,并不影响应力。
二、应力函数取二次多项式
,应力分量。
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to ,ponents
Conclusion: The stress function can used to solute the problem of uniformly distributed shearing stresses rectangular plate.(Fig3-1b)
-1
(a)
(b)
(c)
Two-dimensional Problems in Rectangular Coordinates
Conclusion: stress function can be used to solute the problem of uniformly distributed tensile(if ) pressive(if ) stresses on y-axis of rectangular plate.(Fig3-1a)
2
ax
=
j
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平面问题的直角坐标解答
结论:应力函数能解决矩形板在方向受均布拉力(设)或均布压力(设)的问题。如图3-1(a)。
,应力分量。
结论:应力函数能解决矩形板受均布剪力问题。如图3-1(b)。
图3-1
(a)
(b)
(c)
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Stress Function in the form of a Polynomial of the Third Degree
The Co