Geometric Nonlinear Analysis Properties and Materials
Special element types and nonlinear materials are available for geometric nonlinear analysis.
As a general rule property and material definitions that are only applicable in geometric nonlinear analysis are defined on extensions to the original property and to a MAT1 material, respectively. The extensions are grouped with the base entry by sharing the same PID or MID. In the case of a subcase that is not a geometric nonlinear analysis, these extensions are ignored. Property defaults can be set for shells (XSHLPRM) and solids (XSOLPRM) that may replace the use of property extensions.
Property example:
PSHELL, 3, 7, 1.0, 7, , 7 PSHELLX, 3, 24, , , 5
Material example:
MAT1, 102, 60.4, , 0.33, 2.70e-6
MATX02, 102, 0.09026, 0.22313, 0.3746, 100.0, 0.175
Coordinate Systems
In geometric nonlinear analysis there are moving and fixed coordinate systems. Rectangular coordinate systems that are defined thru grid points (CORD1R, CORD3R) are moving with the deformations of the model. Systems defined in terms of point coordinates (CORD2R,
CORD4R) are fixed.
The behavior of loads depends on the coordinate system referenced. If the loads FORCE, MOMENT are desired to be follower forces, a CID that references a moving coordinate system (CORD1R, CORD3R) must be defined. Otherwise these loads are not following the
deformation. PLOAD always follows the deformations.
Difference Between Geometric Linear and Geometric Nonlinear Analysis
In geometric linear analysis all deformations and rotations are small (infinitesimal). As a general rule, displacements of say 5% of the model dimension and rotations up to 5 degrees can be treated as small. Rotations are trickier. A rotating body seems to get bigger linearly under deformation even if defined as rigid. Nonlinearities can only come from contact or materials. This type of analysis is supported in Nonlinear Quasi-Static Analysis with
ANALYSIS = NLSTAT. Loads stay in the undeformed coordinates and simply move along the
axis they are defined in.
In geometric nonlinear analysis, displacements and rotations are large (finite). The magnitude of a force actually matters. Changes in magnitude of a load can change convergence behavior considerably. Also the direction of a force needs to be controlled.
Forces may follow the deformation or keep their direction. This can be controlled thru the choice of coordinate systems (see above).
The images below display two examples of these differences. Figure 4 shows a cantilever beam solved with small displacements, large displacements with a follower force, and large displacements without a follower force. Figure 5 shows a simple rigid rotated by an angle solved with small and finite rotations.
Figure 4: Cantilever beam with small (GLIN) and large (GNL) displacements
Figure 5: Small (GLIN) vs. finite (GNL) rotations
Difference Between Implicit and Explicit Analysis Implicit static analysis has the following characteristics:
Involves matrix factorization
Stiffness matrix must be positive definite
- Model must be sufficiently constraint - No unattached parts
Iteration is needed to reach equilibrium
Equilibrium is achieved within iteration tolerances Larger time steps
Long-term, (quasi-)static events
Implicit dynamic analysis has the following characteristics:
Involves matrix factorization
Dynamic stiffness matrix must be positive definite Iteration is needed to reach equilibrium
Equilibrium is achieved within iteration tolerances Larger time steps
Long-term events
Explicit (dynamic) analysis has the following characteristics:
In general a diagonal mass matrix is used No matrix factorization necessary
Equilibrium is always guaranteed
Maximum stable time step needs to be respected Small time steps
Short-term events
Implicit Contact
In an implicit contact analysis, you need to take care of the following two concerns:
First, there should be no initial penetrations in the mesh. Sometimes, initial penetration is necessary to begin the simulation then only a small (< 0.01*GAP) value is recommended to not change reality too much. With high initial penetrations, the solution will progress but may lead to incorrect results. You will be warned about initial penetration during the check run.
Secondly, in quasi-static analysis the model needs to be sufficiently constrained. For example, having two blocks on top of each other (Figure 6) the top part is not constrained.
It is recommended to have the meshes completely depenetrated and to define a very small GAP. This would create small springs constraining the upper body in vertical direction. Of course, the other rigid body motions of the part have to be constrained too.
More information can be found in CONTACT, CONTPRM, and PCONTX bulk data definitions.
Figure 6: Initial GAP
Implicit Snap-thru, Post-buckling Analysis
Some nonlinear problems with large deformations encounter bifurcations. The solution becomes instable and the structure buckles or snaps from one state to another (Figure 7).
The load vs. displacement does not simply increase but may reduce until another stable point is reached from which the load then can continue to increase (Figure 8). In the implicit solution procedure it is clear that a simple load increment may not be sufficient to determine the point where the force starts reducing.
A special method needs to be employed to find the proper search direction s for the solution to stay on its path. This solution is called Riks method and can be defined via NLPARMX, SACC. The search direction is defined by satisfying certain constraints of which two methods can be selected via NLPARMX, CTYP.
There are currently some limitations in the way the results are written. Internal forces cannot be plotted yet.
Figure 7: Snap-thru
Figure 8: Snap-thru - Load vs. displacement
Not Sufficiently Constrained Model in Implicit (Quasi-)static Analysis
For models that are not sufficiently constrained, inertia stiffness can be used to overcome a singular stiffness matrix (NLPARMX, KINER = ON). The inertia stiffness, Kinertia = 1 / (DTSCQ * dt)2M, is added to the stiffness matrix K in a (quasi-)static analysis. Care needs to be taken in the selection of DTSCQ. An added mass that is too large may lead to incorrect results. This function is similar to inertia relief in other analysis types.