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.
Object-Oriented Programming for Scientific Codes. II: Examples in C++
This paper illustrates some specific numerical code applications using an object-oriented programming (OOP) paradigm. It is the second of two papers describing OOP issues for scientific-code development. A brief description is given of an object library as well as some simple finite difference and finite element user codes based on that library. The key to efficient OOP implementation in any environment is to conceive an effective object-oriented design of the physical problem and its mathematical abstraction in the first place. This design places a premium on understanding the physical problem from the perspective of class structure, inheritance, and communication. Some of the issues that must be addressed prior to the development of a truly successful OOP environment for large-scale scientific code development and employment are discussed. Optimization issues of OOP in general and the object-oriented programming language C++ in particular are discussed. Our research suggests that there is a tremendous potential for OOP as a development environment for scientific codes.