When the load on the structure reaches a certain value, if a small increment is added, the equilibrium configuration of the structure will change greatly. This phenomenon is called structural instability into structural buckling.
According to the nature of instability, structural stability problems can be divided into the following three categories:
The first kind of instability is an idealized situation, that is, when a certain load is reached, besides the original equilibrium state of the structure, the second kind of equilibrium state is derived, so the meaning is called the branch point instability of the balanced bifurcation unstable member, and the mathematical treatment is to solve the eigenvalue problem, so the meaning is called eigenvalue buckling analysis. When the structure is unstable, the corresponding load can be called buckling load, critical load, buckling load or balanced branch load. For example, the instability of perfect (flawless and straight) central compression column, middle compression plate, flexural member and compression column shell all belong to the first type of instability.
When the second kind of unstable structure is unstable, the deformation will develop for everyone, and there will be no new deformation form, that is, the equilibrium state will not change qualitatively, which is also called pole instability. When the structure is unstable, the corresponding load is called ultimate load or crushing load. Without an ideal mattress or finished animal structure, there will always be some defects, such as initial bending, residual stress, load position deviation and so on. The instability of most structures lies in the second kind of instability problem.
The second instability is that when the load reaches a certain value, the equilibrium state of the structure suddenly jumps to another non-adjacent equilibrium state with a large displacement. This instability is called Snop—-crossing instability. There is no equilibrium bifurcation point or extreme point in jump instability, such as the instability of flat arch, shallow shell, shallow reticulated shell structure and two-force bar. Because the structure may be destroyed when jumping, it is generally impossible to adopt unstable state.
Structural elastic stability analysis belongs to the first kind of instability problem, and its purpose is to solve the critical load value. The corresponding analysis type in ANSY3 is eigenvalue buckling analysis. The second kind of instability and the second kind of instability problems correspond to the static nonlinear analysis of structures in ANSYS, which can be completed at one time regardless of the pre-buckling equilibrium state or the post-buckling equilibrium state.
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Get, that is, "the whole process analysis".
This chapter introduces the related technologies of ANSYS eigenvalue buckling analysis. Unless otherwise specified in this chapter, "buckling analysis" used alone refers to "eigenvalue buckling analysis".
In the stable equilibrium state, considering the influence of axial force or internal force in the middle plane on bending deformation, the equilibrium equation of the structure is obtained according to the principle of potential energy standing value.
The main steps of eigenvalue buckling analysis are as follows:
(1) Create a model,
(2) obtaining a static solution:
(3) obtaining the deformation of the eigenvalues,
4 inspection results,
Create a model
The modeling of eigenvalue buckling analysis is not different from most analyses, but the following three points should be noted:
(1) The instrument considers the line behavior. If a nonlinear element is defined, it will be regarded as a linear element. Stiffness calculation is based on the initial state and remains unchanged in subsequent calculations. For example, if the contact element is included, its stiffness is calculated based on the state after static prestress analysis and will not change.