Simulation based design please help and do all three parts. If possible identify

Question

Simulation based design please help and do all three parts.
If possible identify which book is it taken from! strong 1 1 Norma. Emphasis Heading Subtitle Styles Paragraph Question 3: 1. The coordinates of Node 1, 2 A triangle element with 3 nodes is shown in the figure of and 3 are (0, 1), (0, 0) and (1,00, respectively. The deflections along xand y axis Nodes 1, 2, 3 are (uh,v1),(u2,v2) and (u,,v), respectively. deflection functions of (1) Try to use the nodal deflections ofthese 3 nodes to build this triangle element, that is, u(x,y) and v(x,y). Hints: Assume u x,y) and v(x,y) are a linear function of x and y, that is, a box+ cy Then use the deflections of 3 nodes to determine a, b and c. (2) Express the deflection functions u(x, y) and (x, y) by shape functions. o, calculate the strain 0.02, v 0) and (u 0, 0.01), 0, Em and E at point (0.5,0.5) av(x, y) Qu(x, y) Hints: use equations E E Node 1 (ur vo (0,1) Node 3 (u, v (0.0) Node 2 (u, Figure 1 A 3 node triangle element

Explanation / Answer

solution:

1)for given system we have following data as follows

for poit 1

A(0,1),u1=0,v1=0.01

B(0,0),u2=0,v2=0

C(1,0),u3=0.02,v3=0

here for x direction deflection function is given by

u=a+bx+cy

putting three condition we get three equation as

a+c=0

a=0

a+b=.02

solving we get that

a=0,b=.02,c=0

sofunction as u(x,y)=.02x

for y direction deflection we have that

V=a+bx+cy

0.01=a+c

0=a

0=a+b

from this we get that

a=0,b=0,c=.01

v(x,y)=.01y

so two equation are

u=.02x

v=.01y

3)where strain is given by

exx=du/dx=.02

eyy=dv/dy=.01

4)where shape function in 2 D is given by

u=N1u1+N2u2+N3u3

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