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Nonlinear Control Slideline The augmented Lagrangian method with slidelines employs both penalty parameters (contact stiffnesses) and Lagrangian multipliers to reduce contact penetrations. At convergence, the method checks the penetrations against a tolerance. If any are outside the tolerance the Lagrangian multipliers, and if the penalty update procedure is specified, the contact stiffnesses are updated at the relevant nodes and the solution is rerun. The progress of the solution is controlled by the SLIDELINE data section, which places a limit on the number of Lagrangian multiplier and penalty parameter updates. SLIDELINE NAGLMX NPUPMX Naglmx Npupmx Maximum number of augmented Lagrangian updates per increment (default = 2). Maximum number of penalty parameter (contact stiffness) updates per increment (default = 1). Application of Loads with Nonlinear Control The stress state is always 'remembered' on iteration zero after a change of control. In a nonlinear analysis the stresses will be updated based on the external loads until convergence is achieved. If the load is reduced to zero in a subsequent loadcase, then the resulting stresses may also reduce to zero while any plastic strains will remain. The type of loading is important when determining whether a load level from one increment is "remembered" or " forgotten" in subsequent increments when using manual or automatic load incrementation (see also General Loading Rules). Some loading types are total in nature whilst other are incremental. All of the loading types in LUSAS are total with the exception of the Incremental Prescribed Displacement loading type (PDSP) Total These apply only the specified loading magnitude to the structure. This means that any previously specified loading at a node or element is overwritten by the current specification of load. Consider an automatic, fixed load increment in which a concentrated load magnitude of 5.0 is to be incremented from a reference load factor of 0.2 over 3 increments. The initial load applied will be calculated according to 0.2*5.0. The subsequent two load increments will be calculated as 0.4*5.0 and 0.6*5.0 Incremental The specified loading magnitude is applied in addition to the load already applied to the structure. Consider the example above but with incremental prescribed displacement loading. The initial load applied will be calculated according to 0.2*5.0. The 321
