in a finite element system,three displacement x,y,z are known to satisfy.?

Question

solve the equation to find the unknown displacement x,y,z

7x+7y+3z=2
5x+4y+3z=1
6x+3y+5z=-4

Answer 1

I'm guessing that this is a system of 3 equations and 3 unknowns. There are several ways to do this. You can use linear algebra, algebraic substitution, or Excel. To solve by Excel,

You need to solve the following linear algebra expression:

AX = B where,

A = matrix of coefficients
X = matrix of variables
B = matrix of answers

To solve for X, you need to calculate the inverse of A:

X = (A^-1)(B)

Now, create a 3x3 block with the variable coefficients:

7, 7, 3
5, 4, 3
6, 3, 5

Label this block. To do this, go to INSERT->NAME->DEFINE. Call it 'A'

Do the same for B, but this time only highlight a 3x1 block.

Now calculate the inverse of A. To do this, highlight an empty 3x3 block and type the following formula:

=MINVERSE(A)

Also, make sure that you press CTRL+ALT+ENTER simultaneously after typing the formula. This tells Excel that the operation you are performing is a array/matrix type. I got the following for the inverse of A:

11, -26, 9
-7, 17, -6
-9, 21, -7

Again, label this matrix, let's call it 'INVERSE'

To solve for X, we need to use another formula:

=MMULT(INVERSE, B)

Again, highlight a 3x1 empty block and enter the formula, remembering to press CTRL+ALT+ENTER simultaneously. I get the following answer for X:

-40
27
31

This means that x = -40, y = 27, z = 31

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Hope this helps