Abstract
Abstract
An inverse mosaic method, a geometric mapping for a triangular element followed by mesh smoothing, has been proposed. The main difference between this and the original geometric mapping method lies in the type of element by which the final deformed shape is defined. In fact, the quadrilateral element is less dexterous than the triangular element for a description of surface shape, and describable surface shape using only the quadrilateral element is quite limited. Because of this problem, original geometrical mapping has limited applications to relatively simple shapes. Since the present inverse mosaic method is based on the triangular element, the method is applicable to most surfaces regardless of the complexity of the shape. Moreover, polygons can be divided into several pieces of triangles; the method can be applied to the finite element mesh system generated by a mesh generator, where quadrilateral elements and triangular elements are mixed together. Accuracy and dependence on the order of determination are also significant problems. In the inverse mosaic method, the accuracy has been improved markedly through smoothing after mapping, sufficient for it to be used for the actual problems, e.g. trim-line design. In spite of these marked improvements, the accuracy is basically limited, especially when the involved deformation mode is mainly by drawing or stretching, rather than bending, since deformation behaviour has not been accounted for. In general, the accuracy of an iterative scheme is better than the retromarching scheme, e.g. geometric mapping for optimal blank design; however, the method requires an initial guess to start the iterative sequence. Both the accuracy and the initial guess generation have been solved by combining the present inverse mosaic method and the radius vector method, a kind of iterative method. The efficiency has been verified through deep-drawing examples.