A generative design technique for exploring shape variations

Because innovative and creative design is essential to a successful product, this work brings the benefits of generative design in the conceptual phase of the product development process so that designers/engineers can effectively explore and create ingenious designs and make better design decisions. We proposed a state-of-the-art generative design technique (GDT), called Space-filling-GDT (Sf-GDT), for the creation of innovative designs. The proposed Sf-GDT has the ability to create variant optimal design alternatives for a given computer-aided design (CAD) model. An effective GDT should generate design alternatives that cover the entire design space. Toward that end, the criterion of space-filling is utilized, which uniformly distribute designs in the design space thereby giving a designer a better understanding of possible design options. To avoid creating similar designs, a weighted-grid-search approach is developed and integrated into the Sf-GDT. One of the core contributions of this work lies in the ability of Sf-GDT to explore hybrid design spaces consisting of both continuous and discrete parameters either with or without geometric constraints. A parameter-free optimization technique, called Jaya algorithm, is integrated into the Sf-GDT to generate optimal designs. Three different design parameterization and space formulation strategies; explicit, interactive, and autonomous, are proposed to set up a promising search region(s) for optimization. Two user interfaces; a web-based and a Windows-based, are also developed to utilize Sf-GDT with the existing CAD software having parametric design abilities. Based on the experiments in this study, Sf-GDT can generate creative design alternatives for a given model and outperforms existing state-of-the-art techniques.     

Bridging qualitative spatial constraints and feature-based parametric modelling: Expressing visibility and movement constraints

We present a concept for integrating state-of-the-art methods in geometric and qualitative spatial representation and reasoning with feature-based parametric modelling systems. Using a case-study involving a combination of topological, visibility, and movement constraints, we demonstrate the manner in which a parametric model may be constrained by the spatial aspects of conceptual design specifications and higher-level semantic design requirements. We demonstrate the proposed methodology by applying it to architectural floor plan layout design, where a number of spaces with well defined functionalities have to be arranged such that particular functional design constraints are maintained. The case-study is developed by an integration of the declarative spatial reasoning system CLP(QS) (CLP(QS) – a declarative spatial reasoning system. www.spatial-reasoning.com.) with the parametric CAD system FreeCAD.     

A practical generative design method

A generative CAD based design exploration method is proposed. It is suitable for complex multi-criteria design problems where important performance criteria are uncomputable. The method is based on building a genotype of the design within a history based parametric CAD system and then, varying its parameters randomly within pre-defined limits to generate a set of distinctive designs. The generated designs are then filtered through various constraint envelopes representing geometric viability, manufacturability, cost and other performance related constraints, thus reducing the vast design space into a smaller viable design space represented by a set of distinctive designs. These designs may then be further developed by the designer. The proposed generative design method makes minimal imposition on the designer’s work process and maintains both flexibility and fluidity that is required for creative design exploration. Its ability to work seamlessly with current CAD based design practices from early conceptual to detailed design is demonstrated. The design philosophy behind this generative method and the key steps involved in its implementation are presented with examples.     

Adaptive and variant design of rotational connections

When producing technical documentation for rolling rotational connections, more time is used for drawing preparation than for actual problem-solving. The major share of element development is made using adaptive or variant design methods. Computer support can shorten the time needed. The designer must be careful not to lose the overview of the problem. Efficient CAD systems should provide the designer with: a high degree of creative work, possibility of adaptations of form, technology and regulations over wide limits, and high reliability and constant control over the design process. This paper studies the possibilities of the design process methods related to the capabilities of such an intelligent CAD system used for the design of rotational connections and workshop documentation for the purposes of manufacture.     

A Geometric Unification of Constrained System Dynamics

A unified geometric formulation of the methods used for solving constrained system problems is given. Both holonomic and nonholonomic systems are treated in like manner, and the dynamic equations are expressible in either generalized velocities or quasi-velocities. Moreover, a wide range of unconstrained systems are uniformly regarded as generalized particles in the multi-dimensional metric spaces relating to their configuration. The derivation is grounded on the tensor calculus formalism and appropriate geometric interpretations are reported. In its useful matrix form, the formulation turns out short, elementary and general. This unified geometric approach to constrained system dynamics may deserve to become a generally accepted method inacademic and engineering applications.     

Divergent exploration in design with a dynamic multiobjective optimization formulation

Formulation space exploration is a new strategy for multiobjective optimization that facilitates both divergent exploration and convergent optimization during the early stages of design. The formulation space is the union of all variable and design objective spaces identified by the designer as being valid and pragmatic problem formulations. By extending a computational search into the formulation space, the solution to an optimization problem is no longer predefined by any single problem formulation, as it is with traditional optimization methods. Instead, a designer is free to change, modify, and update design objectives, variables, and constraints and explore design alternatives without requiring a concrete understanding of the design problem a priori. To facilitate this process, we introduce a new vector/matrix-based definition for multiobjective optimization problems, which is dynamic in nature and easily modified. Additionally, we provide a set of exploration metrics to help guide designers while exploring the formulation space. Finally, we provide an example to illustrate the use of this new, dynamic approach to multiobjective optimization.     

传统绘图系统的几何约束驱动关键技术研究及实践

文中针对如何在传统绘图系统中拓展几何约束驱动功能，以实现面向设计师的灵活的参数化设计问题，对几何数据的转换，几何约束识别、表达、筛选及求解进行了较系统的探讨，提出了经实际检验行之有效的技术实现方法，特别地对具有独创性的约束识别的实施进行了阐述     

Solving Interval Constraints by Linearization in Computer-Aided Design

Current parametric CAD systems require geometric parameters to have fixed values. Specifying fixed parameter values implicitly adds rigid constraints on the geometry, which have the potential to introduce conflicts during the design process. This paper presents a soft constraint representation scheme based on nominal interval. Interval geometric parameters capture inexactness of conceptual and embodiment design, uncertainty in detail design, as well as boundary information for design optimization. To accommodate under-constrained and over-constrained design problems, a double-loop Gauss-Seidel method is developed to solve linear constraints. A symbolic preconditioning procedure transforms nonlinear equations to separable form. Inequalities are also transformed and integrated with equalities. Nonlinear constraints can be bounded by piecewise linear enclosures and solved by linear methods iteratively. A sensitivity analysis method that differentiates active and inactive constraints is presented for design refinement.     

An approximation-concepts approach to shape optimal design

In the past, much of the work done in structural optimization consisted in resizing the members of fixed configuration models. In that case, a powerful design procedure has now emerged, which is based on the coordinate use of explicit high-quality approximations of the behavior constraints and dual methods of mathematical programming.There is, however, a large class of problems for which the main degrees of freedom for the designer correspond to the shape of the structure itself.The main objectives of this paper are to recall briefly a convenient geometric representation, in which the boundaries of the structure are represented by Bezier or B-spline curves, and then to discuss the choice of optimization algorithm. It is shown that cost-efficient methods for structural sizing may be advantageously extended to shape optimal design problems. Different approximation schemes are tested and a new general optimization algorithm is presented that combines mixed approximations and dual methods. Many large-scale applications are treated to demonstrate the generality and the efficiency of the new formulation. Finally, considerations are given about an integrated approach including CAD computer codes and finite element optimization software.     

Computer-Aided Construction of Finite Geometric Spaces: Automated Verification of Geometric Constraints

The category of noncommutative geometric spaces is a rather new and wide field in geometry that provides a rich source of hard computer applications. In this contribution we give a short summary of the basic notions of geometric spaces. The so-called parallel map that describes a space will play a fundamental role because, in terms of the parallel map, a geometric space can be represented in such a way that geometric conditions/axioms (which form the structure of a space) are expressible by certain equations. To verify a configuration amounts to showing the solvability of a corresponding equation or a system of equations, respectively. This is a computational aspect that opens the whole field naturally to computer applications by means of automated deduction in geometry, verification of geometric constraints, computer-aided construction of finite geometries. We give motivation why we use specific declarative programming languages for doing all the implementations and computer applications.     

基于SolidWorks-MATLAB-ANSYS集成框架的结构设计优化

在基于仿真模型的结构设计优化中,需要多次进行几何建模和仿真分析,耗费设计人员大量的工作时间。单一的软件不能或者难以完成几何建模、仿真分析及优化求解等工作,有效集成多种软件对产品进行参数化建模、仿真和设计优化是解决这一问题的有效手段。针对上述问题,提出一种SolidWorks-MATLAB-ANSYS集成框架,分别利用MATLAB的优化计算能力、SolidWorks的几何建模能力和ANSYS的有限元分析能力,以MATLAB为主程序,调用SolidWorks/ANSYS进行参数化几何建模和仿真分析。该集成框架能将设计人员从重复建模和仿真工作中解放出来。以一种微型飞行器机身的结构设计为例,说明了该方法的有效性。     

自由曲线在参数化设计中的应用

对与自由曲线有关的几何约束种类进行比较全面地研究,讨论了自由曲线应用到参数化设计系统中后几何约束的求解问题,提出可以用基于图的自由度分析方法对几何约束问题进行分解,介绍了简单凝聚模式下有关自由曲线几何约束的凝聚计算问题.     

产品反求工程中基于几何特征及约束的模型重建

由于大多数机械零件产品都是按一定特征设计制造的,同时特征之间具有确定的几何约束关系,因此,在产品的模型重建过程中,一个重要的目标即是还原这些特征以及它们之间的约束,具体方法是首先进行特征识别,将测量数据分块,然后基于特征约束建立优化数学模型,在建模过程中寻求满足特征参数目标函数下的约束最优解,使重建模型更为准确、接近原型。     

Reliability-based design optimization for elastoplastic mechanical structures

In this paper, two special formulations to carry out a reliability-based design optimization of elastoplastic mechanical structures are introduced. The first approach is based on a well-known two-level method where the first level involves the optimization for the design parameters whereas the evaluation of the probabilistic constraints is carried out in a sub-optimization level. Because the evaluation of the probabilistic constraints in a sub-optimization level causes non-convergence behavior for some problems as indicated in the literature, an alternative formulation based on one-level is developed considering the optimality conditions of the β-computation by which the probabilistic constraint appears in the first level reliability-based design optimization formulation. In both approaches, an explicit parameter optimization problem is proposed for the computation of a design point for elastoplastic structures.Three examples in this paper demonstrate that the one-level reliability-based design optimization formulation is superior in terms of convergence to an optimal design than the two-level reliability-based design optimization formulation.     

Introducing solid objects into a constraint modelling system

A constraint modelling system called RASOR allows the constraints between design parameters to be investigated by a designer. Some simple geometric entities are provided. The ACIS solid modeller provides procedures for handling solid objects. An integrated system in which ACIS solids are defined and manipulated by RASOR commands has been achieved. The use of constraints is illustrated with reference to the assembly of the links of a mechanical system.     

BendCad: a design system for concurrent multiple representations of parts

Concurrency in product design and manufacturing process planning is supported in a recently developed sheet metal design system that incorporates preliminary process design at the detail product design stage. This new design with process features approach represents the evolving part form to the designer in multiple process domains and at multiple stages of a sequential process. Each set of part form representations defines the conceptualized process that transforms it from one to the other. At this modeling level, processes are reversible so that design activity can take place in any of the domains and be transferred to the others. We have fully implemented this concept in a sheet metal design/manufacturing system in which preliminary process design occurs concurrently with product design and the normal representational ambiguities of wireframe and flat panel models are eliminated.     

几何约束满足的统一模型

几何约束满足是参数化设计中的中心问题,研究了陈述和构造统一的约束满足策略,通过将冗余约束转化为形状自由度的方法解决了构造序列的约束闭环问题,采用剪枝和凝聚相结合的策略实现了欠约束和完备约束系统的分解,并在参数化设计与绘图系统ＭＤＳ４．０上实现。     

Variable chromosome length genetic algorithm for progressive refinement in topology optimization

This article introduces variable chromosome lengths (VCL) in the context of a genetic algorithm (GA). This concept is applied to structural topology optimization but is also suitable to a broader class of design problems. In traditional genetic algorithms, the chromosome length is determined a priori when the phenotype is encoded into the corresponding genotype. Subsequently, the chromosome length does not change. This approach does not effectively solve problems with large numbers of design variables in complex design spaces such as those encountered in structural topology optimization. We propose an alternative approach based on a progressive refinement strategy, where a GA starts with a short chromosome and first finds an optimum solution in the simple design space. The optimum solutions are then transferred to the following stages with longer chromosomes, while maintaining diversity in the population. Progressively refined solutions are obtained in subsequent stages. A strain energy filter is used in order to filter out inefficiently used design cells such as protrusions or isolated islands. The variable chromosome length genetic algorithm (VCL-GA) is applied to two structural topology optimization problems: a short cantilever and a bridge problem. The performance of the method is compared to a brute-force approach GA, which operates ab initio at the highest level of resolution.     

Pushing Convertible Constraints in Frequent Itemset Mining

Recent work has highlighted the importance of the constraint-based mining paradigm in the context of frequent itemsets, associations, correlations, sequential patterns, and many other interesting patterns in large databases. Constraint pushing techniques have been developed for mining frequent patterns and associations with antimonotonic, monotonic, and succinct constraints. In this paper, we study constraints which cannot be handled with existing theory and techniques in frequent pattern mining. For example, avg(S)v, median(S)v, sum(S)v (S can contain items of arbitrary values, {<, <, , } and v is a real number.) are customarily regarded as tough constraints in that they cannot be pushed inside an algorithm such as Apriori. We develop a notion of convertible constraints and systematically analyze, classify, and characterize this class. We also develop techniques which enable them to be readily pushed deep inside the recently developed FP-growth algorithm for frequent itemset mining. Results from our detailed experiments show the effectiveness of the techniques developed.     

On design of joint positions for minimum mass 3D frames

An iterative procedure for determining the joint positions and dimensions of cross-sections corresponding to a minimum mass space frame is presented. Stress constraints, displacement constraints and side constraints are taken into account, with the possibility for linking of the design variables, which in addition to the joint positions are the beam dimensions. The frame is assumed to carry consecutively a number of different systems of loads, including temperature loads and weights. The stressed state analysis includes tension, bending, shear and torsion of the beam elements.The optimization iteration includes a sequence of quadratic programming problems with the possibility of move-limits. Only nearby constraints (active strategy) are considered, and analytical expressions for the gradients are derived. Illustrative medium scale problems are presented.