MegaStructures
Structural
- Sep 26, 2019
- 376
Hello:
I'm trying to understand the physical significance of the matrix analysis method of calculating Euler buckling load employed in Finite Element programs. I feel like I am very close, but can't quite grasp the last bit.
From what I understand linear buckling is calculated by using the following formula
([Kt]+λ*[Kg])*{μ}=0
where Kt is the "base" stiffness matrix of the original elements and Kg is the stress stiffness matrix, which is created by the effect of forces. When ([Kt]+λ*[Kg])=0 then the structure has no stiffness and can buckle from any perturbation.
What I don't understand is how a compressive load reduces the stiffness of the individual elements. I get the Euler buckling is calculated based on the bending strength of the beam and the critical buckling load is the axial load that, if applied at an infitecimal eccentricity, would exceed the beams bending resistance, makes sense, but this matrix solution is confusing me more than it should.
Anybody want to take a crack at explaining Kg to me?
“The most successful people in life are the ones who ask questions. They’re always learning. They’re always growing. They’re always pushing.” Robert Kiyosaki
I'm trying to understand the physical significance of the matrix analysis method of calculating Euler buckling load employed in Finite Element programs. I feel like I am very close, but can't quite grasp the last bit.
From what I understand linear buckling is calculated by using the following formula
([Kt]+λ*[Kg])*{μ}=0
where Kt is the "base" stiffness matrix of the original elements and Kg is the stress stiffness matrix, which is created by the effect of forces. When ([Kt]+λ*[Kg])=0 then the structure has no stiffness and can buckle from any perturbation.
What I don't understand is how a compressive load reduces the stiffness of the individual elements. I get the Euler buckling is calculated based on the bending strength of the beam and the critical buckling load is the axial load that, if applied at an infitecimal eccentricity, would exceed the beams bending resistance, makes sense, but this matrix solution is confusing me more than it should.
Anybody want to take a crack at explaining Kg to me?
“The most successful people in life are the ones who ask questions. They’re always learning. They’re always growing. They’re always pushing.” Robert Kiyosaki