Strand7: Hints & Tips
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Nonlinear analysis - setting up the load table
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In nonlinear analysis the loads are applied incrementally; that is the load is stepped up gradually and convergence achieved at each level of load before applying more load. This is necessary to ensure stability and convergence of the solution.
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Many new users of the nonlinear solver are unsure of the requirements for setting up this load table. There are basically three things that must be considered - the number of increments, the number of iterations and the proportion of the load that is applied in each increment.
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For a typical civil/structural engineering problem where nonlinear P-D effects are to be considered the load table will typically only have about 3-4 increments. Such problems only involve small nonlinearities since the deflections are still fairly small. On the other hand structures that involve complex nonlinearities such as buckling or structures with large deflections, (eg. membranes), can require many increments.
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The exact number of increments required for a particular problem is difficult to estimate and must really be determined by the experience of the user and/or trial and error.
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The number of iterations required must be sufficient to ensure convergence for a given load increment. The number of iterations specified by the user only defines the maximum number at which the solution is terminated for a particular load increment. Of course if the solution converges in fewer interations then only those iterations actually required are carried out.
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The most difficult part of the load table to get right is the magnitude of the load factors. In many cases it is sufficient to divide the load equally between the different load increments. However this may not provide optimum convergence and in some cases may not allow the solution to converge at all. If you do not have a feeling for the required magnitude of the load increments then you probably should start with equal load increments.
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There are many types of nonlinear analysis where a constant load step is not desirable. An example is a problem that involves nonlinear buckling. The model can initially be loaded quite rapidly until the load level is just below the buckling load. As the buckling load is approached the size of the load steps is reduced until very small steps are used to capture the formation of the buckle.
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Another case where nonuniform stepping is essential is in the solution of some cable and membrane problems. This type of problem requires a table which is the opposite of that required for the buckling problem. The cable or membrane initially has no lateral stiffness and the load is applied in small steps to allow the deflection and hence stiffness of the structure to develop gradually. Once the structure has assumed the basic deformed shape the loads can be applied more rapidly.
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Clearly, setting up the load table requires a knowledge of the function of the table and also of the likely behaviour of the structure. It is obviously a task that will become easier when the user has had some experience. To a certain extent the load table requires a degree of experimentation on the part of the user. Even experienced users will find it necessary to experiment a little to achieve optimum convergence for a particular problem.
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Automatic load stepping
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Strand7 includes an automatic load reduction capability for nonlinear analysis. It may be possible to apply the load in large increments and rely on Strand7 to automatically reduce this load when steps are experiencing difficulty in converging. You can also choose whether the sub-increments are saved or not. This setting is available in the Defaults tab of the nonlinear solver.
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