Biswajit，

谢谢回复。

如果我考虑一个小问题;作为轴对称模型的正方形(在3D中产生圆柱体)。材料模型是粘弹性的。如果我在上表面和下表面上有一条线，并将上表面压到大约一半的高度，下表面固定(接触分析，没有摩擦)，我得到一个变形的矩形。我用ANSYS和我的FEA代码在FORTRAN做同样的事情。发生的事情是:

没有NLGEOM ON，我得到了与我的代码和ANSYS完全匹配，但体积不守恒。使用NLGEON ON，我得到一个略大的矩形，在这种情况下，体积在ANSYS中是守恒的。

我也想在我的FEA代码中保存体积，因此我试图了解我需要在我的FEA代码中做什么修改?我的有限元代码遵循Newton Raphson方法和与ANSYS相同的算法进行粘弹性应力计算。 I am stuck in my research because of this. Please guide me with whatever you know.

Thanks,

Shriram

Research Assistant
Structural and Multidisciplinary Optimization Lab.

University of Florida

NLGEOM命令激活校正大的刚体旋转和翻译时，使用小的张力本构关系。它也被激活为大应变材料模型。有关实现的详细信息，请参见第3章。ANSYS理论手册中的几何非线性结构。

使用NLGEOM对是否满足不可压缩性条件没有影响。不可压缩性通常使用拉格朗日乘子方法来满足，这只能导致数值代码中不可压缩性的近似满足。然而，有一些应力更新算法可以精确地满足不可压缩性，通常是通过使用指数映射(参见Weber和Anand, 1988年左右)。下面是ANSYS手册中的剪切/粘贴作业。

——Biswajit

大旋转

如果旋转很大，但机械应变(引起应力的机械应变)很小，则可以使用大旋转程序。 A large rotation analysis is performed in a static (ANTYPE,STATIC) or transient (ANTYPE,TRANS) analysis while flagging large deformations (NLGEOM,ON) when the appropriate element type is used. Note that all large strain elements also support this capability, since both options account for the large rotations and for small strains, the logarithmic strain measure and the engineering strain measure coincide.

3.3.1. Theory

Large Strain presented the theory for general motion of a material point. Large rotation theory follows a similar development, except that the logarithmic strain measure ((Equation 3–6)) is replaced by the Biot, or small (engineering) strain measure: (3–37)where: [U] = stretch matrix [I] = 3 x 3 identity matrix 3.3.2.

Implementation

A corotational (or convected coordinate) approach is used in solving large rotation/small strain problems (Rankin and Brogan(66)). "Corotational" may be thought of as "rotated with". The nonlinearities are contained in the strain-displacement relationship which for this algorithm takes on the special form:(3–38)where: [Bv] = usual small strain-displacement relationship in the original (virgin) element coordinate system [Tn] = orthogonal transformation relating the original element coordinates to the convected (or rotated) element coordinates

The convected element coordinate frame differs from the original element coordinate frame by the amount of rigid body rotation. Hence [Tn] is computed by separating the rigid body rotation from the total deformation {un} using the polar decomposition theorem, (Equation 3–5). From (Equation 3–38), the element tangent stiffness matrix has the form: (3–39)and the element restoring force is: (3–40)where the elastic strain is computed from: (3–41) is the element deformation which causes straining as described in a subsequent subsection.

The large rotation process can be summarized as a three step process for each element:

Determine the updated transformation matrix [Tn] for the element.

Extract the deformational displacement from the total element displacement {un} for computing the stresses as well as the restoring force .

After the rotational increments in {Δu} are computed, update the node rotations appropriately.

All three steps require the concept of a rotational pseudovector in order to be efficiently implemented (Rankin and Brogan(66), Argyris(67)).

Chandra，

谢谢回复。

我在ANSYS帮助菜单中找不到技术细节。你说的理论手册是指“帮助”部分还是其他什么?请让我知道。

再次感谢。

Shriram

它使用Hencky或对数应变测量，即ln(U)，其中U是变形梯度极坐标分解得到的正确拉伸矩阵。在计算Hencky应变时，它使用u的特征值和特征向量。你可以在ANSYS理论手册中阅读更多内容，有一章是关于结构非线性的。

Chandra Veer Singh