4832.sagews

#求解质量阵,文献1的公式10a, 10b
# [1] Finite-element method for large-amplitude two-dimensional panel flutter at hypersonic speeds.pdf

w1, s1, w2, s2, x = var('w1, s1, w2, s2, x ')
#形函数
N1=1-3*x*x+2*x*x*x
N2=x*(1-2*x+x*x)
N3=3*x*x-2*x*x*x
N4=x*x*x-x*x
#形函数1阶导数
N1d1=6*x*x-6*x
N2d1=3*x*x-4*x+1
N3d1=6*x-6*x*x
N4d1=3*x*x-2*x
#形函数2阶导数
N1d2=12*x-6
N2d2=6*x-4
N3d2=6-12*x
N4d2=6*x-2

f1=N1
f2=N2
f3=N3
f4=N4

mm11=f1*f1
mm12=f1*f2
mm13=f1*f3
mm14=f1*f4

mm21=f2*f1
mm22=f2*f2
mm23=f2*f3
mm24=f2*f4

mm31=f3*f1
mm32=f3*f2
mm33=f3*f3
mm34=f3*f4

mm41=f4*f1
mm42=f4*f2
mm43=f4*f3
mm44=f4*f4

m11=integral(mm11, x, 0, 1)
m12=integral(mm12, x, 0, 1)
m13=integral(mm13, x, 0, 1)
m14=integral(mm14, x, 0, 1)

m21=integral(mm21, x, 0, 1)
m22=integral(mm22, x, 0, 1)
m23=integral(mm23, x, 0, 1)
m24=integral(mm24, x, 0, 1)

m31=integral(mm31, x, 0, 1)
m32=integral(mm32, x, 0, 1)
m33=integral(mm33, x, 0, 1)
m34=integral(mm34, x, 0, 1)

m41=integral(mm41, x, 0, 1)
m42=integral(mm42, x, 0, 1)
m43=integral(mm43, x, 0, 1)
m44=integral(mm44, x, 0, 1)

print m11;print m12;print m13;print m14
print m21;print m22;print m23;print m24
print m31;print m32;print m33;print m34
print m41;print m42;print m43;print m44

show(m11);show(m12);show(m13);show(m14)
show(m21);show(m22);show(m23);show(m24)
show(m31);show(m32);show(m33);show(m34)
show(m41);show(m42);show(m43);show(m44)

13/35 11/210 9/70 -13/420 11/210 1/105 13/420 -1/140 9/70 13/420 13/35 -11/210 -13/420 -1/140 -11/210 1/105

$$\renewcommand{\Bold}[1]{\mathbf{#1}}\frac{13}{35}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}\frac{11}{210}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}\frac{9}{70}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}-\frac{13}{420}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}\frac{11}{210}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{105}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}\frac{13}{420}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{140}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}\frac{9}{70}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}\frac{13}{420}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}\frac{13}{35}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}-\frac{11}{210}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}-\frac{13}{420}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{140}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}-\frac{11}{210}$$

$$\renewcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{105}$$