In this paper, an analytic solution is presented using differential transform method (DTM) for a class of wave equation. The emphasis is on the nonlinear two-dimensional wave equation. The procedures introduced in this paper are in recursive forms which can be used to obtain the closed form of the solutions, if they are required. The method is tested on various examples, and the results reveal ...

In this study we deal with the two-dimensional non-guillotine cutting problem of how to cut a set of larger rectangular objects to a set of smaller rectangular items in exactly a demanded number of pieces. We are concerned with the special case of the problem in which the non-used material of the cutting patterns (objects leftovers) may be used in the future, for example if it is large enough t...

This paper discusses some of the basic formulation issues and solution procedures for solving oneand twodimensional cutting stock problems. Linear programming, sequential heuristic and hybrid solution procedures are described. For two-dimensional cutting stock problems with rectangular shapes, we also propose an approach for solving large problems with limits on the number of times an ordered s...

Efficient cutting design is essential to reduce the costs of production in the open die forging industry. This article discusses a slab cutting design problem that occurs when parallel piped items are cut from raw material steel slabs with varying widths and lengths to meet a volume requirement. The problem is modeled as a two-dimensional cutting stock problem or bin packing problem with size-c...

The technology of the artificial neural network (ANN) was applied in the research of supercritical material cutting. Two-dimensional Gaussian surfaces of the three cutting elements and workpiece surface hardness had been established fitting through JMP software. Base on the orthogonal milling experiments, the rules of cutting forces variation were forecasted, as well as the effect to the hardne...

In this paper, an integer programming model for two-dimensional cutting stock problems is proposed. In the problems addressed, it is intended to cut a set of small rectangular items of given sizes from a set of larger rectangular plates in such a way that the total number of used plates is minimized. The two-stage and three-stage, exact and non-exact, problems are considered. Other issues are a...

We analyze the properties of an interior point cutting plane algorithm that is based on a semi-infinite linear formulation of the dual semidefinite program. The cutting plane algorithm approximately solves a linear relaxation of the dual semidefinite program in every iteration and relies on a separation oracle that returns linear cutting planes. We show that the complexity of a variant of the i...