ANSYS分析结果中的各种应力(Stress)类型

在Ansys Workbench的分析结果中，有很多种Stress可选，如下图所示。那么这些Stress到底都是什么意思呢，摘录相关帮助文件如下：

Ansys Help帮助文件中的相关路径为：

ANSYS Documentation> Mechanical Applications> Mechanical User’s Guide> Using Results> Structural Results> Stress and Strain

1.Equivalent(von-Mises)等效应力(冯米塞斯应力)

等效应力的可由三个主应力通过下述公式计算获得：

Equivalent stress is related to the principal stresses by the equation:

Equivalent stress (also called von-Mises stress) is often used in design work because it allows any arbitrary three-dimensional stress state to be represented as a single positive stress value. Equivalent stress is part of the maximum equivalent stress failure theory used to predict yielding in a ductile material.

等效应变计算公式如下：

The von-Mises or equivalent strain ε_e is computed as:

ν' = effective Poisson's ratio, which is defined as follows:where:

Material Poisson's ratio for elastic and thermal strains computed at the reference temperature of the body.

0.5 for plastic strains.

2.Maximum/Middle/Minimum Principal第一/第二/第三主应力

From elasticity theory, an infinitesimal volume of material at an arbitrary point on or inside the solid body can be rotated such that only normal stresses remain and all shear stresses are zero. The three normal stresses that remain are called the principal stresses:

根据弹性力学理论，任意无限小体积均可以找到仅有正应力，而剪切应力为零的状态，此时的主应力按照从大到小的顺序排列，分别称为第一、第二、第三主应力。

σ1 - Maximum

σ2 - Middle

σ3 - Minimum

The principal stresses are always ordered such that σ₁ > σ₂ > σ₃.

3.Maximum Shear最大切应力

The maximum shear stress τ_max, also referred to as the maximum shear stress, is found by plotting Mohr's circles using the principal stresses:

or mathematically through:

For elastic strain, the maximum shear elastic strain γ_max is found through:

γ_max = ε₁ - ε₃

since the shear elastic strain reported is an engineering shear elastic strain.

4.Intensity应力强度

Stress intensity is defined as the largest of the absolute values(最大绝对值) of σ₁-σ₂, σ₂-σ₃, or σ₃-σ₁:

Stress intensity is related to the maximum shear stress:

σ_I = 2τ_max

Elastic Strain intensity is defined as the largest of the absolute values(最大绝对值) of ε₁ - ε₂, ε₂ - ε₃, or ε₃ - ε₁:

Elastic Strain intensity is equal to the maximum shear elastic strain:

ε_I= γ_max

Equivalent Stress (and Equivalent Elastic Strain) and Stress Intensity

Note: Computation of Equivalent Elastic Strain uses Poisson’s ratio. If Poisson’s ratio is temperature dependent then the Poisson’s ratio value at the reference temperature of the body is used to compute the Equivalent Elastic Strain.

5.Normal正应力

方向可选X，Y, Z.

6.Shear切应力

方向可选XY,YZ,XZ.

7.Vector Principal向量主应力

A Vector Principals plot provides a three-dimensional display of the relative size of the principal quantities (stresses or elastic strains), and the directions along which they occur. Positive principals point outwards and negative ones inwards.

Plots of Vector Principals help depict the directions that experience the greatest amount of normal stress or elastic strain at any point in the body in response to the loading condition. The locus(轨迹) of directions of maximum principal stresses, for example, suggests paths of maximum load transfer throughout a body.

Request a Vector Principals plot in the same way that you would request any other result. Scoping is also possible. Numerical data for these plots can be obtained by exporting the result values to an .XLS file. These files have 6 fields. The first three correspond to the maximum, middle, and minimum principal quantities (stresses or elastic strains). The last three correspond to the Mechanical APDL application Euler angle sequence (CLOCAL command in the ANSYS environment) required to produce a coordinate system whose X, Y and Z-axis are the directions of maximum, middle and minimum principal quantities, respectively. This Euler angle sequence is ThetaXY, ThetaYZ, and ThetaZX and orients the principal coordinate system relative to the global system. These results can be viewed using the Graphics button, so that you can use the Vector Display toolbar.

8.Error误差

You can insert an Error result based on stresses to help you identify regions of high error and thus show where the model would benefit from a more refined mesh in order to get a more accurate answer. You can also use the Error result to help determine where Mechanical will be refining elements if Convergence is active. The Error result is based on the same errors used in adaptive refinement. Information on how these errors are calculated is included in POST1 - Error Approximation Technique, in the Theory Reference for ANSYS and ANSYS Workbench.

Note:  The Error result is based on linear stresses and as such may be inaccurate in certain nonlinear analyses (for example, when plasticity is active). Furthermore, the Error result is currently restricted to isotropic materials. You may wish to refer to the Structural Material Properties section of the Engineering Data help for additional information.

Presented below are example applications of using the Error result in a Structural simulation.

3D Model:

2D Model, Base Mesh:

2D Model, Adaptive Refinement (Convergence Added):

2D Model, With Mesh Control:

9.Membrane Stress薄膜应力

Membrane stress calculates the stresses along the thickness of the shell in longitudinal direction, in transverse direction, and in plane shear. The result is available only for shell bodies and solids that are meshed using the thin-solid meshing option(薄膜应力仅对壳体或者使用薄实体单元网格划分选项的实体有效). Each element of the body can display individual stress values and give a checkboard appearance to the result contours. The results are calculated in the element coordinate system.

Shell membrane stress tensor (s11m, s22m, s12m) is the average of the in-plane stress tensor (s11(z), s22(z), s12(z)) along the shell thickness direction:

Where:

t is the total shell thickness,

z is the thickness location where the in-plane stress is evaluated.

Unlike linearized stress in other elements, a pre-defined path through the shell thickness is not required in order to compute shell membrane stress.

Note:Make sure that the Output Control, General Miscellaneous is set to Yes or your results may be under-defined.

10.Bending Stress弯曲应力

The result is available only for shell bodies and solids that are meshed using the thin-solid meshing option(弯曲应力仅在壳体或者使用薄实体单元网格划分选项的实体时可选) and are calculated in the element coordinate system. Each element of the body can display individual stress values and give a checkboard appearance to the result contours.

Shell bending stress tensor (s11b, s22b, s12b) represents the linear variation portion of the in-plane stress tensor (s11(z), s22(z), s12(z)) along the shell thickness direction:

Where:

t is the total shell thickness,

z is the thickness location where the in-plane stress is evaluated.

Note: Make sure that the Output Control, General Miscellaneous is set to Yes or your results may be under-defined.