Engineering | Finite Element Analysis | Stress
© Copyright Value Design Consulting Ltd
Value Design
Consulting
Non-Linear Buckling
A more practical approach is to carry out a large displacement analysis, where buckling can be detected by the change of displacement in the model. A large displacement problem is non-linear in nature. Geometric non-linearity arises when deformations are large enough to significantly alter the way load is applied, or load is resisted by the structure. The approach to a non-linear buckling solution is achieved by applying the load slowly (dividing it into a number of small loads increments). The model is assumed to behave linearly for each load increment, and the change in model shape is calculated at each increment. Stresses are updated from increment to increment, until the full applied load is reached. The solution becomes an iterative procedure rather than one of matrix factorisation alone, and consequently is computationally expensive. An interesting variation arises in the case of automotive applications. In the case of front end collision, the hood is expected to crumple (buckle) in order to absorb the energy of collision, as well as to save the passenger compartment. In such cases, we are not designing against, but for buckling.
Avoiding Instabilities
Any structure is most efficient when subjected to evenly distributed tensile or compressive
stress, such as occurring in cables, strings etc. Evidently, such modes of loading
makes the best use of the material, and its strength. On the other hand bending (flexing)
is the least efficient way of loading a structure. A high flexural stiffness of the
structure means high resistance to buckling. This is true even if the load is entirely
in-plane, since when buckling is imminent, the only stiffness that counts is flexural.
Eccentricity of loading promotes buckling. Eccentricity means that the resultant
load does not pass through the centroid of the load bearing cross section. It is
safe to assume that in 100% of practical applications, loads are eccentric. When
buckling occurs, symmetry of the part does not apply. There is no symmetry of the
buckled shape, although both the part, and the loading may be symmetric. Correspondingly,
when carrying out an FE buckling investigations, it is advisable to implement a full
3D analysis of the structure under inspection.
The non-linear stress strain behaviour
of the material reduces the stiffness at higher stress (load) levels, and hence elastic
formulas from the handbooks tend to be highly un conservative. If a component is
structurally slender, and is made of plastic, then the component faces buckling from
three directions; from the low material stiffness, large deflections producing eccentricity
during deformation, and non-linearity of the material itself.
Buckling - nonlinear
Navigate the knowledge base
