Load Optimisation for Air Bending in the Context of Damage Reduction

Abstract

Load optimisation applied to air bending is used to optimise the damage state in the formed component. In [1], elastomer bending is presented, where superposed stresses due to the reaction forces of the elastomer cushion lead to reduced damage growth. Replacing the elastomer cushion with compressive loads allows for optimisation of these loads such that the damage, estimated with the stress triaxiality, is reduced. The optimisation is accomplished with the commercial FEM-Software Abaqus as the solver for the mechanical problem where Sequential Quadratic Programming (SQP) is used within Matlab to generate improved loads.The results obtained in [1], where damage evolution in selected forming processes was investigated, show the possibilities of superimposing stresses in bending to yield lesser damaged components, while maintaining the same deformation and final shape. The disadvantage of the elastomer cushion, however, is the inhomogeneous triaxiality distribution and the impossibility to directly define the forces imposed by the elastomer. The objective of load optimisation is to generate loads which yield a reduced damage state and, to later on improve the elastomer cushion for a precise setup of the reaction forces. Theory of load optimizationThe main idea for load optimisation has been presented in e.g. [2]. There, the external loads f within the equilibrium condition of the finite element formulationcan be optimised to generate new improved loads for a given problem. For the optimisation, the external loads are replaced by polynomial functions, with the coefficients of the polynomial as the design variables for the optimisation. Numerical implementationThe main part of this work is the implementation of the optimisation framework. For the sake of comparison with the results in [1], the software Abaqus is used as the solver for the FEM problem. This allows for the use of the same material properties as well as the in-built contact formulations. With this in mind, the optimisation framework is built around Abaqus in order to allow mathematical optimisation. For the optimisation, Matlab is used with its solver quadprog for SQP. In order to transfer the data from the simulations for the optimisation within Matlab, the python library and interface provided by Abaqus are utilised.The problem is defined in the Complete Abaqus Environment (CAE) and includes the region for the objective function, the area for the side constraints and the nodes for the load application. The input file created this way can then be altered to allow for optimisation. The complete optimisation framework consists of the following steps:1. Run a structural analysis (Abaqus) for the material response of the problem with design variables s.2. Perturb design variable s i (Matlab) and calculate the structural response (Abaqus) and the numerical gradient for the corresponding design variable via finite differences.3. Use the objective functions, side constraints and gradients for SQP and generate a new design (Matlab).For the mathematical optimisa...

Numerical optimisation of damage in extrusion processes

“…This approach is an extension to the implementation in [13, 14]. In this initial concept, applied to air bending, the input‐file (.inp) of the simulation problem was directly modified to incorporate design changes.…”