Cutting Pattern Generation Research Articles

Arbitrary Lagrangian-Eulerian formulations for cutting pattern generation of tensile membrane structures

ABSTRACT An application of Arbitrary Lagrangian-Eulerian (ALE) method is used to generate the cutting pattern shapes of membrane structures. The initial patterning panels are selected as the projection of three-dimensional (3D) membrane panels and are assumed as the reference configuration. While the Lagrangian displacements define the forced displacements from this configuration to the 3D configuration, the Eulerian terms describe the motion from this reference configuration to the current patterning panels. The cutting pattern panels can be determined by this process considering the effect of prescribed pre-stress and material properties. Several examples are performed to point out the effectiveness of the proposed method on simplifying the cutting pattern process and the reduction in the stress deviation from the intended pre-stress.

CAD-Integrated Parametric Lightweight Design With Isogeometric B-Rep Analysis

The complex geometries of lightweight structures can easily be modeled with modern CAD systems that use NURBS. Isogeometric B-Rep Analysis (IBRA) adopts the NURBS geometries along with their topology for the analysis model, which can thus fulfill both design purposes and solve structural problems in one software environment. Especially in lightweight design, which is characterized by a strong interaction between shape and structural behavior, this presents a major advantage. Results can be used as a new input to consecutive analyses within this novel approach. This is especially useful for the simulation of construction stages or in the design cycle of membrane structures, where mechanically driven optimizations such as formfinding and cutting pattern generation, as well as structural analysis, are dependent on each other. This paper focusses on parametric design with IBRA and the advantages of the uniform model description and workflow. Not only geometrical but also mechanical properties can be parameterized and thus offer a large variety of options to explore for designers as well as engineers. In addition to the possibility of optimization through formfinding methods, the provided framework can conveniently be combined with other tools and thus be extended by external optimization loops where geometry and structural parameters are modified simultaneously. The successful integration of parametric IBRA in a CAD environment such as Rhino and Grasshopper is presented. Selected examples demonstrate the significance of the CAD-integrated unified workflow for the interactive analysis loops of lightweight structures.

A new patterning technique of membrane structures for minimizing deviations of stress and shape

Abstract For cutting pattern generation of membrane structures, non-developability of doubly curved surfaces can cause deviations of stress and shape, which directly influence bearing capacity and structural integrity of final structures. Thus, cutting errors should be diminished as much as possible for precise-forming of membrane structures, especially for airships and air-supported structures as formwork. This paper proposes a new patterning technique to generate the optimized cutting pattern, which is based on a multi-objective optimization concept for simultaneously minimizing the deviations of stress and shape from design. Using the coordinates of 2D elements as key variables, the proposed method performs a geometrically nonlinear finite element analysis based on the initial cutting pattern iteratively. This approach can effectively reduce the deviations of stress and shape of the whole structure by reducing the stress deviation of 2D strips. The validity of the method is examined by the comparison of numerical results, which shows that the actual equilibrium stress is closer to design stress than that of existing works, and the shape distortion is almost negligible.

CAD-integrated Parametric Design Cycle for Structural Membranes

The design cycle of membrane structures consists of three interactive and highly non-linear disciplines. Formfinding is performed in order to find a geometry that allows the prestressed structure to carry loads through tension only. Once a formfound geometry is set, structural analysis needs to assess the structure's safety and usability. The most challenging step is the cutting pattern generation, which aims at finding the planar pieces which can be elevated to build spatial membrane structures with a minimum deviation from the desired shape and prestress state.<br/> Isogeometric B-Rep Analysis (IBRA) allows the designer to perform analyses on the original CAD model without leaving the CAD environment. High quality is ensured for the geometry and the mechanical approximation by using Non-Uniform Rational B-Splines (NURBS). Additionally, the topology information of multipatches can be transferred to the analysis in order to enrich the design space. Trimmed and coupled surfaces can thus be included in the analysis. Parametric models allow the designer to examine a large variety of geometrical and mechanical entities with one model.<br/> The advantages of the CAD-integration with IBRA for the highly interactive design of structural membranes are shown in this contribution.

Computational Cutting Pattern Generation Using Isogeometric B-Rep Analysis

The cutting pattern plays a major role for the design of structural membranes, since it influences both their aesthetical appearance and structural behavior.A novel approach towards cutting pattern generation is the so-called Variation of Reference Strategy (VaReS) [1], which minimizes the total potential energy arising from the motion of a planar cutting pattern to its corresponding three-dimensional shape.With non-uniform rational B-Splines (NURBS) being the standard tool for geometry description in CAD, it is only consequent to use these for analysis as well. Isogeometric B-Rep Analysis (IBRA) [2] follows up on this idea and enriches the original Isogeometric Analysis (IGA), which was introduced by Hughes et al. [3], by the possibility of analysing trimmed NURBS geometries.This paper presents cutting pattern generation with the Variation of Reference Strategy in the context of IGA/IBRA. With this approach, the whole design of a membrane structure can be represented by NURBS geometries – including blueprint plans. To use the benefits of IBRA for cutting pattern generation, a NURBS-based membrane-element was developed for the VaReS routine.A developable surface serves as a benchmark example, since its analytical cutting pattern is known. Examples of double-curved geometries show the applicability and benefits of the proposed procedure for real structures.

Cutting patterns of membrane structures

Membrane structures are very lightweight and highly optimized structures. Due to the constant stress state, strength of materials is used optimally. In order to prevent the occurrence of large deformations even for small external loads, membrane structures are designed as a double curved surfaces and are stabilized by applying prestress. Minimal surfaces has zero mean curvature and the basic advantage is that the stress at all points and directions is equal and there are no extreme stresses anywhere on the surface. Also have minimal area for the given contour, so the weight and amount of material is reduced to minimum, which make them suitable for application in architecture. Practical realization involve process of cutting pattern generation, which divide surfaces in parts that are developable surfaces. When patterns are assembled and prestressed they provide three-dimensional surface. Ideally, the cutting lines should follow the geodesics lines. We use geodesics as the shortest path between two points on a surface. In the article we give method for finding shortest paths on polygonal representations of surfaces follows continual Dijkstra paradigm which, on some conditions, can give improved accuracy on a computer despite the restriction of available memory and execution time.

Smooth cutting pattern generation technique for membrane structures using geodesic line on subplane and spline interpolation

Practical techniques for smooth geodesic patterning of membrane structures were investigated. For the geodesic search, adjustment of the subplane of the extracted elements series was proposed, and various spline approximation methods were used to flatten the strip for the generation of a smooth pattern. This search approach is very simple, and the geodesic line could be easily attained by the proposed method without the need for a difficult computation method. Smooth cutting patterning can also be generated by spline approximation without the noise in discrete nodal information. Additionally, the geodesic cutting pattern saved about 21% of the required area for the catenary model due to the reduction of the curvature of the planar pattern seam line.

Symmetry preserving in Topological Mapping for tension structures

When using Topological Mapping (TM) together with the Force Density Method (FDM) in order to find a first form of equilibrium for a tension structure whose fixed nodes coincide in plan view with the vertices of a regular polygon, it has been observed that the symmetry may be lost. The problem is related to the mapping procedure that is introduced in the process. However, if some rules are followed in constructing the topology for the mesh, the symmetry can be preserved. With a symmetric mesh, the later cutting pattern generation process becomes simpler, easier, and cheaper. This paper will provide one simple algorithm that has been proved to work effectively in preserving the symmetry in the cited type of tension structures. Several examples are presented in order to better illustrate the applicability of these easy prescriptions.

Implementation of genetic algorithm for optimum cutting pattern generation of wrinkle free finishing membrane structures

The purpose of this paper is to show a practical implementation of a genetic algorithm for minimizing membrane stresses discrepancies between the actual assembled equilibrium and the specified design state. The method prevents the surface wrinkle problems in membrane structures under service loading and determines an optimum cutting pattern, which accounts for the designed stresses of the membrane structures. Using the displacements of the 3-D surface as the key variables, the proposed method utilizes a geometrically nonlinear finite element analysis based upon the improved the stress-adapted numerical form finding of pre-stressed surfaces by the updated reference strategy. The model of genetic algorithm and the genetic operators are then designed to solve numerically the optimization problem. The method is validated through examples and compared with the available data. The analysis results show no significant differences between the assumed designed stresses and the actual stresses in the membrane.

스플라인 곡선을 이용한 막구조물의 재단도 작성에 관한 연구

막 구조물은 일반적인 설계와는 달리 형상해석, 응력변형해석 및 재단도 과정을 수행하여야만 설계가 가능하다. 처음 두 과정과는 달리 재단은 3차원 곡면을 최소 오차를 가진 평면 스트립을 형성하는 과정이다. 경제적인 이유로 재단 선은 주로 측지선을 이용하여 작성된다. 그러나 일반적으로 측지선은 초기 형상탐색에서 구성된 삼각형 요소의 정보에서 추출됨으로 부드러운 곡선이 아니며, 불규칙한 직선이다. 그러므로 어떻게 불규칙한 직선을 곡선으로 표현할 것인가가 중요하다. 따라서 본 연구에서는 스플라인 함수를 이용한 보간 방법을 재단도 생성에 적용하였다. 이를 위해서 삼차 스플라인 함수, B-스플라인 함수 및 최소자승 스플라인 함수의 세 가지 경우에 대해서 고찰하고, 단순 모델 및 카테나리 모델을 대상으로 재단도 작성 결과를 검토하였다. 단순모델의 해석요소수와 추출된 불연속 절점 수에 따른 보간 곡선 비교결과는 요소수가 큰 경우 추출된 절점의 수가 적은 것이 효과적이며, 최소자승 보간이 다른 방법보다 더 부드러운 재단 경계선을 제공한다. For membrane structure, there are three main steps in design and construction, which are form finding, statistical load analysis, and cutting patterning. Unlike the first two stages, the step of cutting pattern involves the translation of a double-curved surface in 3D space into a 2D plane with minimal error. For economic reasons, the seam lines of generated cutting patterns rely greatly on the geodesic line. Generally, as searching regions of the seam line are plane elements in the step of shape analysis, the seam line is not a smooth curve, but an irregularly divided straight line. So, it is how we make an irregularly divided straight line a smooth curve that defines the quality of the pattern. Accordingly, in this paper, we analyzed interpolation schemes using spline, and apply these methods to cutting pattern generation on the curved surface. To generate the pattern, three types of spline functions were used, i.e., cubic spline function, B-spline, and least-square spline approximation, and simple model and the catenary-shaped membrane was adopted to examine the result of generation. The result of comparing the approximation curves by the number of elements and the number of extracted nodes of simple model revealed that the seam line for less number of extracted nodes with large number of elements were more efficient, and the least-square spline approximation provided smoother seam line than other methods.

A New Method of Cutting Pattern

The geodesic method is the most practical and economical method of cutting pattern generation. In this paper, a new method to generate the geodesic is proposed. The arithmetic of the method is simple and practicable, and it overcomes the deficiency of geometrical method.

A Forest-Level Bucking Optimization System that Considers Customer's Demand and Transportation Costs

Abstract This article describes a system that deals with a forest-level bucking optimization problem considering customer's demand and transportation costs. The system was used to evaluate three scenarios: an observed medium-term forest harvesting scenario, with 32 stands harvested during one month, a simulated demand-oriented scenario and a simulated supply-oriented one. Data was obtained from Pinus taeda L. plantations located in southern Brazil. Various forest multiproducts with their respective local market prices were considered for modeling. The system has two main modules: the Cutting Pattern Generation (CPG) and the Global Bucking Optimization (GBO). In both modules, different algorithms are activated depending on the analyzed scenario (demand-oriented or supply-oriented). Additional biometric modules are also integrated into the system for height, taper, and volume calculations. In the demand-oriented scenario, the CPG exhaustively generates all possible cutting patterns for each diametric class in each stand, and the GBO, formulated as a Mixed Integer Linear Programming problem, optimizes the net revenue at forest level subject to constraints that consider bounds for timber volumes and maximum number of different multiproducts obtained in each stand. In the supply-oriented scenario, the CPG generates the Optimum Cutting Pattern through a heuristic algorithm that identifies the potential cuts to evaluate along the stem and a Dynamic Programming-based algorithm to determine the optimum combination of products that maximizes the stem profit, and the GBO calculates the net profit, summing up the profits per stem for each stand and sum of the stands. Illustrative examples and numerical results are given. FOR. SCI. 48(3):492–503.

A new technique for optimum cutting pattern generation of membrane structures

In general, the cutting pattern for membrane structures is determined by dividing the complicated curved 3-D surface into several 2-D plane strips by using the geodesic line method or flattening technique. In these procedures, however, some discrepancies can occur between actual stresses of equilibrated state and designed uniform stresses initially. These problems mainly arise from the material property and numerical errors. Such deviations can cause unexpected structural problems, thus a precise consideration in the cutting pattern of membrane structures is needed. In this paper, a new analytical method for determining an optimum cutting pattern considering material properties is presented. The optimization method proposed can diminish the deviations occurring from numerical errors as well as from material properties. From the analysis results of the proposed method, it is shown that the final stress distributions for various models are sufficiently closer to design stress distributions than existing ones.

Form Finding and Cutting Pattern Generation for Fabric Tension Structures

Abstract: This paper discusses the problems of form finding and production of cutting patterns for fabric tension strictures. A computer method is proposed for simultaneous form finding and cutting pattern generation which produces initial principal stresses in the directions of the warp and weft of the fabric. A large‐displacement finite element procedure for computing the initial equilibrium shapes of tension structures is presented Several variations on this basic method are suggested. The cutting pattern generation method is based on the finite element model. A weighted least‐squares minimization flattening approach is developed to minimize the change in general link lengths and to generate plane cloth coordinates. Some design examples are given.