# Discussion on geometric nonlinearity in the hottes

2022-09-30
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Discussion on geometric nonlinearity in ANSYS

there are many deformation definitions in ANSYS:

1. Large strain: from the derivation of the ANSYS theory specification, logarithmic strain is introduced. In the original post, this logarithmic strain is considered to be true strain. I think this point is worth discussing. We know that the definition of strain is generally divided into three types, namely engineering strain, or Cauchy strain, that is, the usual definition of strain in the case of small deformation. In the case of large deformation, green strain can be defined based on the initial configuration, and Al strain can be defined based on the actual configuration. 1. For hollow materials such as pipe mansy strain. The author believes that logarithmic strain is actually a strain form defined to simplify large deformation analysis. If the large deformation effect is turned on in ANSYS, the introduction of logarithmic strain is unnecessary, because the difference between the actual configuration and the initial configuration is considered in both Green's strain and almansy's strain. In the small deformation analysis, it is unnecessary to introduce logarithmic strain, because at this time, the difference between the initial configuration and the real configuration is very small, so there is no need to distinguish

however, if the actual deformation is large (more than 10%), and in the analysis, the demand of the food industry for functional films such as high barrier, cooking resistance, UV resistance, light avoidance, antibacterial, breathable, oxygen insulation will continue to increase in the future, and the large deformation effect is not turned on, then it is necessary to use logarithmic strain at this time. (because Cauchy strain is non additive, logarithmic strain is additive). Therefore, logarithmic strain is a strain form of electronic universal testing machine, which is artificially designed to consider large strain without turning on the switch of large deformation effect. The rayon rod drives the sliding sleeve and cross bridge

2。 Large rotation problem

the famous example is the fishing rod problem. Fishing rod is a problem of large deformation and small strain. When the fishing rod is deformed, the deformation that can cause strain is very small, and the large transverse deformation is caused by the rotation of the rigid body. However, in the experimental mechanics of steel pipe scaffold fasteners produced by our company Jinan new period assay instrument Co., Ltd., the treatment of rigid body rotation is very critical. Why is it critical? Because rigid body motion does not produce strain, but for some strain definitions, such as the above engineering strain or logarithmic strain, after directly substituting into the calculation, the strain is not zero (the strain is obtained through displacement), the stress will be calculated. Therefore, it is necessary to eliminate the influence of rigid body motion

the above paragraph is written by sjtu79. The author would like to add that in this case, the best way is to introduce green strain or almansy strain, which can eliminate the influence of rigid body motion (by using green or almansy constitutive rate in the constitutive equation). The stresses corresponding to the above two strains are Kirchhoff stress and Euler stress. The reason why Green's strain is used in finite element analysis is that the initial conditions we know are all for the initial configuration

3。 The geometric nonlinearity of stress stiffing (large deformation, small strain)

this geometric nonlinearity actually considers the influence of the stress state of the previous sub step on the tangent stiffness matrix of the subsequent sub step. When the large deformation effect is turned on, the stress stiffness matrix correction on the sub step level is automatically carried out by the program. At this time, when the stress stiff option is turned on, the author believes that the stiffness matrix correction on the iterative level is turned on, That is, the correction of the stress stiffness matrix to the tangent stiffness matrix is considered in each iteration of the equation

in some linear analysis (such as out of plane deformation of membrane surface), it is necessary to turn on this option. Only when this option is turned on can the influence of in-plane high stress state on out of plane stiffness be considered at the equation iteration level

either logarithmic strain or Green's strain is a strain form defined for the convenience of analysis. The corresponding constitutive relationship can be obtained through uniaxial tensile test (even logarithmic strain is also through elongation λ In general, Cauchy stress logarithmic strain is used in large strain analysis, while Cauchy stress Green strain is used in large rotation (small strain) analysis. The reason why we distinguish between large strain and large rotation (both of them belong to large deformation analysis) is to simplify the analysis

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