Automated design of sheet metal punches for bending multiple parts in a single setup
Sheet metal bending is a process in which bends are formed using a combination of a punch and a die. A very large number of mechanical products such as furniture panels, shelves, cabinets, housing for electro-mechanical devices, etc. are created by using the sheet metal bending process. Bending tools need to satisfy the following two criteria: (1) tools should be able to withstand bending forces, and (2) tool shapes should be such that there is no tool-part interference. In this paper, we describe a methodology for automatically designing shapes of bending punches for bending multiple parts in a single setup. We create parametric geometric models of punches. These parametric models describe the family of possible punch shapes. Using the part geometry and parametric punch shape models, we automatically generated constraints on tool parameters that eliminate the possibility of part-tool interference. We use mixed-integer techniques to identify parameters of punch shapes that result in the maximum punch strength. Finally, we perform strength analysis of the designed punch shape using "nite element analysis methods, to verify that the designed punch shape is capable of withstanding the bending forces. 2001 Elsevier Science Ltd. All rights reserved.
Shape optimal design using B-splines
Abstract Shape optimal design of an elastic structure is formulated using a design element technique. It is shown that Bezier and B-spline curves, typical of the CAD philosophy, are well suited to the definition of design elements. Complex geometries can be described in a very compact way by a small set of design variables and a few design elements. Because of the B-splines flexibility, it is no longer necessary to piece design elements together in order to agree with the shape complexity, nor to restrict the shape variations. Moreover, the additional optimization constraints that are most often needed to avoid unrealistic designs when the shape variables are the nodal coordinates of a finite element mesh, are automatically taken into account in the new formulation. An analytical derivation of the sensitivity analysis will be established, giving rise to numerical efficiency. It will be seen that the resulting optimization problem does not involve highly nonlinear functions with respect to the shape variables, so that simple mathematical programming algorithms can be applied to solve it. Some numerical examples are offered to demonstrate the power and generality of the new approach presented in this paper.
Dual methods for optimizing finite element flexural systems
Abstract Modern numerical methods for the optimization of large discretized systems are now well developed and highly efficient in the case of thin walled elastic structures modeled by finite elements. However, this is not yet true for structures whose components are subject simultaneously to bending and extension loads. In this paper, the idea of Generalized Optimality Criterion (GOC), set forth in previous papers for bar, membrane, and pure bending elements, is extended to deal with general beam and flat shell elements. The modifications brought to the GOC result in explicit approximations for the behavior constraints that are correct up to the first order, but that exhibit a more complex algebraic form. Indeed these explicit expressions are no longer merely linear in the reciprocal design variables. However, they continue to be additively separable, and therefore dual methods remain fully applicable, just as in the original statement of the GOC approach. Numerical examples will be offered to demonstrate the efficiency of the method presented.