Find Exact Solution for Composite Frame Displacements

[math111]

Homework Statement

I need to find the Exact Solution for this problem(Displacements)
I already did it using MATLAB but I need to compare it to the exact solution
I am not sure what equations to use for this problem and where to start?

Homework Equations

-Plane strain
-E and v are given
-no thickness
-length of members are in ( )

The Attempt at a Solution

Break it into four elements and find the force on each side
i.e E2, E3 and E4 have forces pulling but I am not sure what to do about the sharing force for (2) inbetween E3 and E4 and E2 and E4

If anyone can help it would be greatly appreciative

 

[Valkarie]

. The exact solution for this problem would depend on the boundary conditions of the system. For example, if all displacements and rotations are zero at the boundaries, then the solution would be completely determined by the applied forces and moments. If some displacements are known at the boundaries, then the solution would be a combination of the applied forces/moments and the boundary conditions. Without knowing the boundary conditions, it is not possible to determine the exact solution.

 

[Mene]

I would suggest starting by reviewing the equations and theories related to composite frames and their displacements. This could include concepts such as beam theory, strain and stress analysis, and the use of boundary conditions. It may also be helpful to consult with other experts in the field or refer to textbooks and research articles for guidance.

Once you have a solid understanding of the underlying principles, you can use this knowledge to determine the appropriate equations and methods for solving the problem. This may involve breaking the frame into smaller elements and considering the forces and displacements at each point, as mentioned in the attempt at a solution.

It is also important to carefully consider the assumptions and limitations of the problem, such as the given values for E and v, and the assumption of plane strain. This will help ensure that your solution is accurate and applicable to the specific problem at hand.

Overall, finding the exact solution for composite frame displacements requires a thorough understanding of the relevant concepts and careful analysis of the problem. With dedication and attention to detail, you can successfully find the exact solution and compare it to your MATLAB results.