8.3. Using Geometric Nonlinearities

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Small deflection and small strain analyses assume that displacements are small enough that the resulting stiffness changes are insignificant.

In contrast, large strain analyses account for the stiffness changes that result from changes in an element's shape and orientation. By issuing NLGEOM,ON (GUI path Main Menu> Solution> Analysis Type> Sol'n Control ( : Basic Tab) or Main Menu> Solution> Unabridged Menu> Analysis Type> Analysis Options), you activate large strain effects in those element types that support this feature. The large strain feature is available in most of the solid elements (including all of the large strain elements), as well as in most of the shell and beam elements. Large strain effects are not available in the ANSYS Professional program. However, large deflection effects (NLGEOM command) are supported for shell and beam elements in ANSYS Professional, if indicated as such in the Elements Reference.

The large strain procedure places no theoretical limit on the total rotation or strain experienced by an element. (Certain ANSYS element types will be subject to practical limitations on total strain - see below.) However, the procedure requires that strain increments must be restricted to maintain accuracy. Thus, the total load should be broken into smaller steps.

8.3.1. Stress-Strain

In large strain solutions, all stress-strain input and results will be in terms of true stress and true (or logarithmic) strain. (In one dimension, true strain would be expressed as ε = ln ( 0). For small-strain regions of response, true strain and engineering strain are essentially identical.) To convert strain from small (engineering) strain to logarithmic strain, use εln = ln (1 + εeng). To convert from engineering stress to true stress, use σtrue = σeng (1 +  εeng). (This stress conversion is valid only for incompressible plasticity stress-strain data.)

8.3.1.1. Large Deflections with Small Strain

This feature is available in all beam and most shell elements, as well as in a number of the nonlinear elements. Issue NLGEOM,ON (Main Menu> Solution> Analysis Type> Sol'n Control ( : Basic Tab) or Main Menu> Solution> Unabridged Menu> Analysis Type> Analysis Options) to activate large deflection effects for those elements that are designed for small strain analysis types that support this feature.

8.3.2. Stress Stiffening

The out-of-plane stiffness of a structure can be significantly affected by the state of in-plane stress in that structure. This coupling between in-plane stress and transverse stiffness, known as stress stiffening, is most pronounced in thin, highly stressed structures, such as cables or membranes. A drumhead, which gains lateral stiffness as it is tightened, would be a common example of a stress-stiffened structure.

Even though stress stiffening theory assumes that an element's rotations and strains are small, in some structural systems (such as in Figure 8.8: "Stress-Stiffened Beams" (a)), the stiffening stress is only obtainable by performing a large deflection analysis. In other systems (such as in Figure 8.8: "Stress-Stiffened Beams" (b)), the stiffening stress is obtainable using small deflection, or linear, theory.

Figure 8.8  Stress-Stiffened Beams

To use stress stiffening in the second category of systems, you must issue PSTRES,ON (GUI path Main Menu> Solution> Unabridged Menu> Analysis Type> Analysis Options) in your first load step.

Large strain and large deflection procedures include initial stress effects as a subset of their theory. For most elements, initial stiffness effects are automatically included when large deformation effects are activated [NLGEOM,ON] (GUI path Main Menu> Solution> Analysis Type> Sol'n Control ( : Basic Tab) or Main Menu> Solution> Unabridged Menu> Analysis Type> Analysis Options).

8.3.3. Spin Softening

Spin softening adjusts (softens) the stiffness matrix of a rotating body for dynamic mass effects. The adjustment approximates the effects of geometry changes due to large deflection circumferential motion in a small deflection analysis. It is usually used in conjunction with prestressing [PSTRES] (GUI path Main Menu> Solution> Unabridged Menu> Analysis Type> Analysis Options), which is caused by centrifugal force in the rotating body. It should not be used with the other deformation nonlinearities, large deflection, or large strain. Spin softening is activated by the KSPIN field on the OMEGA and CMOMEGA commands (GUI path Main Menu> Preprocessor> Loads> Define Loads> Apply> Structural> Inertiav Angular Velocity).