# Advanced Nonlinear Static, Transient, and Explicit

Solutions 601 and 701

Advanced Nonlinear Solution is a Nastran solution option focused on nonlinear problems

## Overview

- This solution sequence is available with the advanced nonlinear solver.
- Advanced Nonlinear Solution is a Nastran solution option focused on nonlinear problems. It is capable of treating geometric and material nonlinearities as well as nonlinearities resulting from contact conditions. State-of-the-art formulations and solution algorithms are used which have proven to be reliable and efficient.
- Advanced Nonlinear Solution supports static and implicit dynamic nonlinear analysis via Solution 601, and explicit dynamic analysis via Solution 701. Solution 601 also supports heat transfer analysis and coupled structural heat transfer analysis.

- Advanced Nonlinear Solution supports many of the standard Nastran commands and several commands specific to Advanced Nonlinear Solution that deal with nonlinear features such ascontact. The NX Nastran Quick Reference Guide provides more details on the Nastran commands and entries that are supported in Advanced Nonlinear Solution.
- Advanced Nonlinear Solution supports many of the commonly used features of linear Nastran analysis. This includes most of the elements, materials, boundary conditions, and loads. Some of these features are modified to be more suitable for nonlinear analysis, and many other new features are added that are needed for nonlinear analysis.

- The elements available in Advanced Nonlinear Solution can be broadly classified into rods, beams, 2-D solids, 3-D solids, shells, scalar elements and rigid elements. The formulations used for these elements have proven to be reliable and efficient in linear, large displacement, and large strain analyses. Chapter 2 provides more details on the elements.
- The material models available in Advanced Nonlinear Solution are elastic isotropic, elastic orthotropic, plastic bilinear/multilinear, plastic-cyclic, hyperelastic, gasket, nonlinear elastic isotropic, shape memory alloy and viscoelastic. Thermal and creep effects can be added to some of these materials. Chapter 3 provides more details on these material models.
- Advanced Nonlinear Solution has very powerful features for contact analysis. These include several contact algorithms and different contact types such as single-sided contact, double-sided contact, self-contact, and tied contact. Chapter 4 provides more details on contact.
- Loads, boundary conditions and constraints are addressed in Chapter 5. Time varying loads and boundary conditions are common to nonlinear analysis and their input in Advanced Nonlinear Solution is slightly different from other Nastran solutions, as discussed in Chapter 5.
- Solution 601 of Advanced Nonlinear Solution currently supports two nonlinear structural analysis types: static and implicit transient dynamic. Details on the formulations used are provided in Chapter 6. Other features of nonlinear analysis, such as time stepping, load displacement control (arc length method), line search, and available solvers are also discussed in Chapter 6.
- Solution 701 of Advanced Nonlinear Solution is dedicated to explicit transient dynamic analysis. Details on the formulations used are provided in Chapter 7. Other features of explicit analysis, such as stability and time step estimation, are also discussed in Chapter 7.
- Solution 601 of Advanced Nonlinear Solution also supports two heat transfer or coupled structural heat transfer analysis types. The first type 153 is for static structural with steady state heat transfer, or just steady state heat transfer. The second analysis type 159 is for cases when either the structural or heat transfer models are transient (dynamic). This type can also be used for just transient heat transfer analysis. Details of the heat transfer analysis are provided in Chapter 8, and details of the thermo-mechanical coupled (TMC) analysis are provided in Chapter 9.
- Additional capabilities present in Advanced Nonlinear Solution such as restarts, stiffness stabilization, initial conditions, and parallel processing are discussed in Chapter 10.
- Most of the global settings controlling the structural solutions in Advanced Nonlinear Solution are provided in the NXSTRAT bulk data entry. This includes parameters that control the solver selection, time integration values, convergence tolerances, contact settings, etc. An explanation of these parameters is found in the NX Nastran Quick Reference Guide.
- Similarly, most of the global settings controlling the heat transfer or coupled solutions in Advanced Nonlinear Solution are provided in the TMCPARA bulk data entry.

## Choosing Between Solutions 601 and 701

- The main criterion governing the selection of the implicit (Solution 601) or explicit (Solution 701) formulations is the time scale of the solution.
- The implicit method can use much larger time steps since it is unconditionally stable. However, it involves the assembly and solution of a system of equations, and it is iterative. Therefore, the computational time per load step is relatively high. The explicit method uses much smaller time steps since it is conditionally stable, meaning that the time step for the solution has to be less than a certain critical time step, which depends on the smallest element size and the material properties. However, it involves no matrix solution and is non-iterative. Therefore, the computational time per load step is relatively low.

- For both linear and nonlinear static problems, the implicit method is the only option.

- For heat transfer and coupled structural heat transfer problems, the implicit method is the only option.
- For low-speed dynamic problems, the solution time spans a period of time considerably longer than the time it takes the wave to propagate through an element. The solution in this case is dominated by the lower frequencies of the structure. This class of problems covers most structural dynamics problems, certain metal forming problems, crush analysis, earthquake response and biomedical problems. When the explicit method is used for such problems the resulting number of time steps will be excessive, unless mass-scaling is applied, or the loads are artificially applied over a shorter time frame. No such modifications are needed in the implicit method. Hence, the implicit method is the optimal choice.
- For high-speed dynamic problems, the solution time is comparable to the time required for the wave to propagate through the structure. This class of problems covers most wave propagation problems, explosives problems, and high-speed impact problems. For these problems, the number of steps required with the explicit method is not excessive. If the implicit method uses a similar time step it will be much slower and if it uses a much larger time step it will introduce other solution errors since it will not be capturing the pertinent features of the solution (but it will remain stable). Hence, the explicit method is the optimal choice.
- A large number of dynamics problems cannot be fully classified as either low-speed or high-speed dynamic. This includes many crash problems, drop tests and metal forming problems. For these problems both solution methods are comparable. However, whenever possible (when the time step is relatively large and there are no convergence difficulties) we recommend the use of the implicit solution method.
- Note that the explicit solution provided in Solution 701 does not use reduced integration with hour-glassing. This technique reduces the computational time per load step. However, it can have detrimental effect on the accuracy and reliability of the solution.
- Since the explicit time step size depends on the length of the smallest element, one excessively small element will reduce the stable time step for the whole model. Mass-scaling can be applied to these small elements to increase their stable time step. The implicit method is not sensitive to such small elements.
- Since the explicit time step size depends on the material properties, a nearly incompressible material will also significantly reduce the stable time step. The compressibility of the material can be increased in explicit analysis to achieve a more acceptable solution time. The implicit method is not as sensitive to highly incompressible materials (provided that a mixed formulation is used).
- Higher order elements such as the 10-node tetrahederal, 20 and 27 node brick elements are only available in implicit analysis. They are not used in explicit analysis because no suitable mass-lumping technique is available for these elements.
- Model nonlinearity is another criterion influencing the choice between implicit and explicit solutions. As the level of nonlinearity increases, the implicit method requires more time steps, and each time step may require more iterations to converge. In some cases, no convergence is reached. The explicit method however, is less sensitive to the level of nonlinearity. Note that when the implicit method fails it is usually due to nonconvergence within a time step, while when the explicit method fails it is usually due to a diverging solution.
- The memory requirements is another factor. For the same mesh, the explicit method requires less memory since it does not store a stiffness matrix and does not require a solver. This can be significant for very large problems.
- Since Advanced Nonlinear Solution handles both Solution 601 and Solution 701 with very similar inputs, the user can in many cases restart from one analysis type to the other. This capability can be used, for example, to perform implicit springback analysis following an explicit metal forming simulation, or to perform an explicit analysis following the implicit application of a gravity load.
- It can also be used to overcome certain convergence difficulties in implicit analyses. A restart from the last converged implicit solution to explicit can be performed, then, once that stage is passed, another restart from explicit to implicit can be performed to proceed with the rest of the solution.