弹力试卷评分标准.docx

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山东建筑大学试卷答案及评分标准
2012 至2013 学年第 学期 考试时间：120 分钟

(a)Determine the conditions for which(f)(x, y) is an Airy stress
function(that is,for which S(x, y) is biharmonic).
菖粼
题号
1
2
3
4
总分
分数
课程名称： 弹性力学 卷考试形式：（开卷）
年级： 2010 专业: 土木工程；层次：（本科）
1. Determine the stress boundary conditions for the column shown in the figure, where M is the bending moment on the unit width. (25 points).
(b)Derive formulas for the corresponding stress they compatible? (25 points)
Solution
a. Determine the condition that the stress function satisfies the compatibility eqution.
+ 24 = 2/ + 4C + 2E
=0.
(8 points)
Solution:
2. Consider the polynomial
that the stress components can satisfy compatibility equation
= Ax2 + Bxy + Cy2, dx
aV B 2
-= x
dxdy 2
少厂 D 2
2Cxy- — y .
(8 points)
.A 4 B 3 C 2 2 D 3 E 4
(b — —x H—x y H—x y H—xy H y
12 6 2 6 12
b dfx df
『+▽)(?+?) = -(1+〃)顷+丁)
dx dy dx dy
-\2 -\2
= (-^ + -^)(Cx2+W + ^v2+^x2+5xv + Cv2)
dx' dy'
^2C + 2E + 2A + 2C
=(4C + 2E + 2/) = 0
(9 points)
Where (x, y) are plane rectangular coordinates and A,B,C,D,E are constants.
山东建筑大学试卷答案及评分标准
共3页第2页
3. A cantilever, with length I and depth h as well as unit width, is
subjected to the concentrated load p at left face as shown in the figure.
Neglecting body forces,