autodesk equilibrio

1. Activating the command: Setup Model Setup Parameters Advanced Equilibrium
tab
The information on this page applies to the following analysis types except if indicated:
Mechanical Event Simulation (MES)
Static Stress with Nonlinear Material Models
In nonlinear finite element analysis, most iterative solution schemes are based on some
form of the well-known Newton-Raphson iteration algorithm. A detailed description of the
Newton-Raphson scheme may be found in many references, including Hinton, Oden and
Stricklin. The user is also encouraged to review Section 11.5 (pp. 449-452) of Linear and
Nonlinear Finite Element Analysis in Engineering Practice by Constantine C. Spyrakos and
John Raftoyiannis for more discussion on iterative solution schemes.
There are a number of nonlinear iterative solution methods available. (Performing a Riks
analysis sets the iterative solution method.) All the methods are based upon the Newton-
Raphson iteration scheme. You choose from the following methods that display in the
Nonlinear iterative solution method drop-down box:
• Automatic: The processor chooses which iterative solution method based on the other input in
the analysis.
• Full Newton-Raphson method
• Modified Newton-Raphson method
• Combined full-modified Newton-Raphson method
• Full Newton-Raphson method with line search
• Modified Newton-Raphson method with line search
• Combined full-modified Newton-Raphson method with line search
These methods are discussed in more detail below:
Full Newton-Raphson Method
The full Newton-Raphson iterative solution scheme, or the tangent stiffness matrix method,
is the basic form of all the schemes. In this solution scheme the effective stiffness matrix
and the right-hand side effective load vector of the system are reformed or updated for
each equilibrium iteration within all the time/load steps. The advantages of this method are
that it is usually more effective for problems with strong nonlinearity, and that it converges
quadratically with respect to the number of iterations. Since in general the major cost per
equilibrium iteration for nonlinear analysis lies in the construction and factorization of the
effective tangent stiffness matrix, the full Newton-Raphson scheme may be more expensive
in turn of solution time, especially for large-scale problems.
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2. Modified Newton-Raphson Method
The modified Newton-Raphson iterative solution scheme is a procedure that lies in between
the tangent stiffness matrix method (the full Newton-Raphson method) that reforms the
effective stiffness matrix for each equilibrium iteration within all the time/load steps, and
the initial stiffness matrix method (the initial stress method) that constructs and factorizes
the effective stiffness matrix only once. The modified Newton-Raphson method performs the
reformation of the effective stiffness matrix only for the first equilibrium iteration within
each time step, and the rest of the iterations will only involve the updating of the right-
hand side effective load vectors.
Since the modified Newton-Raphson method involves fewer effective stiffness matrix
reformations and factorizations, the computational cost per iteration for the modified
Newton-Raphson method is usually much less than that for the full Newton-Raphson
method. It has been observed that for problems with mild or moderate nonlinearity, for
example, smooth material property or loading condition changes, the modified Newton-
Raphson method is usually more effective. However, for problems with strong nonlinearity,
for example, sudden material property or loading condition changes, this method may
converge very slowly or even diverge.
Combined Full and Modified Newton-Raphson Method
The combined full and modified Newton-Raphson method is between the full Newton-
Raphson method and the modified Newton-Raphson method, and is designed for users who
either have some prior knowledge of the structures at hand or have some advanced
knowledge on nonlinear structural behaviors. You can specify a particular iterative scheme
that may best suit your problem. The full Newton-Raphson and the modified Newton-
Raphson methods are special cases of this method. The default scheme for the combined
full-modified Newton-Raphson method is two right-hand side effective load vector updates
for each effective stiffness matrix reformation.
The latest solution method allows the analysis to achieve convergent solutions for problems
involving motion. This solution method damps out common convergence problems such as
high frequencies, because they are just noise within the solution.
Line Searches
All three solution schemes have the option for line search. Line searching usually helps to
stabilize the iterative schemes. It can be particularly useful for problems involving rapid
changes in structural stiffness due to rapid material property and/or geometric
configuration changes. In such situations line searching usually can accelerate the iterative
process, and sometimes provide convergence where none is obtainable without line
searches. The basic idea behind a line search scheme is the following: During each
equilibrium iterative, the Newton-Raphson method generates a search direction for new
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3. possible solutions, while the line search scheme is used to find a solution in that direction
that minimizes the out-of-balance force error. The convergence tolerance for the line search
can be specified in the Line search convergence tolerance field. This value should be
between 0.4 and 0.6.
Selection of Iterative Solution Scheme
Unlike linear problems, in nonlinear analysis there is no solution scheme that is good for
all kinds of problems. The choice of iterative scheme may be more appropriately chosen for
a particular problem based on the degree of nonlinearity of the problem at hand. Problems
with strong material and geometric nonlinear responses usually require more frequent matrix
reformations. The modified Newton-Raphson method is usually more effective for problems
with smooth material property and/or geometrical configuration changes, while the full
Newton-Raphson method, although more expensive in turn of numerical cost per iteration, is
usually more effective than the modified Newton-Raphson method for problems of strong
nonlinearity. Line searching schemes help an iterative process to converge at sensitive time/
load levels but increase the computational cost per iteration. For a nonlinear analysis where
no prior knowledge is available on the behavior of the structure at hand, the following
procedures are recommended:
1. Start the analysis with the material nonlinear only analysis type and a linear material model,
such as constant material properties. If the material model available for the analysis is
nonlinear, then use the initial values derived from the material model/curves as the constant
material properties. The linear analysis results may not only help to check whether the
geometric, loading and boundary conditions of the system are properly set or imposed, but
may also provide some useful information on the initial response or behavior of the structure
since for small displacements all structures behave linearly. Displacement results from the
linear analysis may also provide a criteria for the selection of reasonable time/load step
increments for the on-going nonlinear analysis.
2. If the original material model is nonlinear, perform the analysis using the material nonlinear
only analysis type. Results from this analysis may help to further understand the behavior of
the structure response and identify some sensitive time/load levels. Moreover, the comparison
of the results from this analysis and those from a large displacement analysis will indicate
whether or not the object has entered a large displacement state. For a structure of small
displacement state, the results from all the three analysis types should be more or less the
same. The time/load level where the results from the three analysis types starts to depart from
each other significantly indicates that the structure has entered large displacement state.
3. With the knowledge obtained from (1) and (2), one may perform the analysis with the Total
Lagrangian or Updated Lagrangian analysis types. If the automatic time step option is used,
the time/load step increments must be reasonably small to represent the material property
and/or geometrical configuration changes of the object during its loading process. If the
multiple time step option is used, one may assign different time/load steps and other
parameters for different time/load zones. For those time/load zones where rapid material
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4. property and geometrical changes may occur, smaller time steps, more frequent matrix
reformations, and line searches are usually required. At some critical time/load levels, such as
bifurcation or collapse time/load levels, it may be necessary to avoid performing matrix
reformations and/or equilibrium iterations or to relax error tolerances near these time/load
levels to observe the pre- or post-buckling/collapse behaviors of the object.
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