Problem in finite element method using direct stiffness method

In summary, the conversation discusses a sample problem from Logan Finite Element Method. The problem involves deriving a stiffness matrix and solving for forces with given boundary conditions. The person is unsure why the force at the third node is assumed to be zero, but it is explained that only one applied force is present at node 4. The solution also states that F4x is equal to 5000 lb. There is a question about whether there should be a reaction at the third node.
  • #1
chiraganand
113
1
Hi,

This is a sample problem from logan finite element method. I have attached the problem and solution given in the book. As per the problem i first derived the stiffness matrix and den putting the boundary conditions started solving for the forces. I am stuck as three forces are unknown but when i checked the book it says the force at third node is zero. Can someone tell me why this force is assumed as zero?
 

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  • #2
F3x = 0 since only one applied force is present in the problem at node 4. So F4x = 5000 lb.
 
  • #3
rock.freak667 said:
F3x = 0 since only one applied force is present in the problem at node 4. So F4x = 5000 lb.
But shudnt there be a reaction at 3rd node
 

1. What is the direct stiffness method in finite element analysis?

The direct stiffness method is a numerical technique used in finite element analysis to solve problems in structural mechanics, such as determining the stresses and displacements of a structure under external loads. It involves breaking down a complex structure into smaller elements and using their stiffness to calculate the overall stiffness of the structure.

2. What are the common problems encountered in the direct stiffness method?

Some common problems encountered in the direct stiffness method include numerical instability, convergence issues, and difficulty in handling large and complex structures. These problems can lead to inaccurate results and require careful consideration and proper implementation of the method to overcome.

3. How can numerical instability be addressed in the direct stiffness method?

Numerical instability in the direct stiffness method can be addressed by using a smaller element size, adjusting the boundary conditions, and using more efficient solution techniques. It is also important to carefully select the element types and properties to ensure stability in the analysis.

4. What are some ways to improve convergence in the direct stiffness method?

To improve convergence in the direct stiffness method, it is important to ensure that the element stiffness matrices are properly formulated and the boundary conditions are accurately applied. Additionally, using adaptive meshing techniques or relaxation methods can also help improve convergence.

5. How does the direct stiffness method compare to other finite element methods?

The direct stiffness method is one of the oldest and most commonly used methods in finite element analysis. It is known for its simplicity and ease of implementation, but it may not be suitable for all types of problems, such as those with nonlinear material behavior. Other finite element methods, such as the finite difference method and the boundary element method, may be more suitable for certain types of problems.

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