A discrete methodology for controlling the sign of curvature and torsion for NURBS

This paper develops a discrete methodology for approximating the so-called convex domain of a NURBS curve, namely the domain in the ambient space, where a user-specified control point is free to move so that the curvature and torsion retains its sign along the NURBS parametric domain of definition. The methodology provides a monotonic sequence of convex polyhedra, converging from the interior to the convex domain. If the latter is non-empty, a simple algorithm is proposed, that yields a sequence of polytopes converging uniformly to the restriction of the convex domain to any user-specified bounding box. The algorithm is illustrated for a pair of planar and a spatial Bézier configuration

Constrained reconstruction of 3D curves and surfaces using integral spline operators

In the context of direct/reverse engineering processes one of the main problem is the reconstruction of curves and surfaces starting from a cloud of points. Most of the times the (re)constructed curves and surfaces have to satisfy some particular geometric constraints and functional properties related to the desired shapes. In this paper, referring to 3D curves and surfaces, we propose an algorithm based on an interpolatory variation diminishing integral spline operator characterized by the presence of shape parameters. In order to choose the best value for the shape parameters different functionals can be adopted. Some test cases are presented in order to show the effectiveness of the proposed algorithm: both academic and real world test cases are considered

CAD interface and framework for curve optimisation applications

Computer Aided Design is currently expanding its boundaries to include more design features in its processes. Design is identified as an iterative process converging to solutions satisfying a set of constraints. Its close relation with optimisation indicate that there is strong potential for the integration of optimisation and CAD. The problem addressed in this thesis lies in interfacing the geometric representation of design with other non-geometric aspects. The example of free-form curve modelling is taken to investigate such relationships. Assumptions are made that Optimisation is powered by Evolutionary Computing algorithms like Genetic Algorithms (GA). The geometric definition of curves is commonly supported by NURBS, whose construction constraints are defined locally at the data points. Here the NURBS formulation is used with GA in an attempt to provide complementary handles on the curves shape other than the usual data point coordinates and control points weights. Differential properties are used for optimising NURBS, Hermite interpolation allows for the definition of higher order constraints (tangent, normal, bi-normal) at data points. The assignment of parameter values at the data points, known as parameterisation also provides control of the curve’s shape. Curve optimisation is also performed at the geometric modelling level. Old mathematical theorems established by Frénet and further developed by other mathematicians provide means of defining a curve’s shape with it’s intrinsic equations. Such representation is possible by using Function Representation (F-rep) algebra available in the ACIS software. Frep allows more generic and exact means of interfacing with the curve’s geometry and new functionality for curve inspection and optimisation are proposed in this thesis. The integration of optimisation findings and CAD are documented in the definition of a framework. The framework architecture proposed reconstructs a new CAD environment from separate elements bolted together in a generic Application Programming Interface (API) named “Oli interface”. Functionality created to interface optimisation and CAD makes a requirement list of the work that both sides should undertake to achieve design optimisation in the CAD environment.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Natural Parameterization

The objective of this project has been to develop an approach for imitating physical objects with an underlying stochastic variation. The key assumption is that a set of “natural parameters” can be extracted by a new subdivision algorithm so they reflect what is called the object’s “geometric DNA”. A case study on one hundred wheat grain crosssections (Triticum aestivum) showed that it was possible to extract thirty-six such parameters and to reuse them for Monte Carlo simulation of “new” stochastic phantoms which possessthe same stochastic behavior as the “original” cross-sections

Topologically reliable approximation of curves and surfaces

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1997.Includes bibliographical references (p. [213]-222).by Wonjoon Cho.Ph.D

Design principles for flexible protection inspired by ancient fish armor of Polypteridae

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 98-101).This thesis is about designing structures that combine the dual functions of mechanical protection and flexibility of motion. The structures are inspired by principles observed in the ganoid squamation (scale assembly) of an ancient fish species called Polypteridae, which first appeared 96 million years ago. Prior work on Polypteridae has focused on understanding the role of the inherent material properties (e.g., stiffness, strength, etc.) of the individual bony scales to provide penetration resistance. Here, geometric design is explored at increasingly larger length scales including 1) morphometric features within individual scales, 2) morphometry of the individual scales as a whole, 3) scale-to-scale interconnections and anisotropic ranges of motion, and, lastly, 4) the entire assembled scale squamation and anisotropic ranges of motion of the entire fish body. Experimental, computational, and mathematical methods employed were micro-computed tomography, microscopy, morphometric analysis, and three-dimensional printing of prototypes. The geometrical design principles discovered were related to biomechanical mobility and protection and then implemented into a generalized, functional design system which possesses similar anisotropic distinctive degrees of freedom and ranges of motion as Polypteridae. The design system offers potential for applications in fields of transportation, military, and architecture.by Steffen H. Reichert.S.M

Topology optimisation and additive manufacturing of structural nodes of gridshell structures

Gridshells, also called lattice shells or reticulated shells, are lightweight spatial structures. Their organic shape, column-free space, free-form surface and maximised transparency have provided limitless design freedom for architects and structural engineers. The design and manufacturing of structural connections (nodes) have been the bottle neck in the design and construction of gridshells, which is due to their complicated geometries and the three-dimensional loading conditions applying on these nodes. The invention of additive manufacturing (AM) provides the possibility of optimising the nodes by using topology optimisation (TO) algorithms. Instead of rationalising the geometry of the nodes to provide simplified connections for conventional production system, custom-designed connections can be achieved with lower weight and higher accuracy using combination of TO and AM. As a consequence, the optimised nodes help reduce the structure size and foundation requirements which leads to saving in the material cost. Furthermore, other features also make the newly designed nodes promising, such as the aesthetical features, high stiffness, high precision and less labour. In this study, Bi-directional Evolutionary Structural Optimisation (BESO) techniques are used to minimise the weight and the printing time required for each node. Firstly, the effect of general load cases on the optimised topology of structural node is studied by comparing the optimised results for the nodes under different individual load cases and combined load cases. Furthermore, the effect of the size of the design-domain on the final weight and topology of a node designed by BESO is examined by using different initial sizes. In addition, various smoothing methods for the final geometry are explored and compared with each other. The challenges of using AM in manufacturing nodes are also investigated through 3D printing individual optimised nodes and the optimised nodes for a case study of a prototype gridshell structure. Besides, comparisons made between optimised nodes and conventional nodes show the efficiency of the optimised nodes. An innovative experimental setup for quasi-static test of nodes under dominant design loads is also proposed in this study. Two nodes are designed and manufactured using BESO and AM to test by a test rig designed based on the proposed setup. In addition, a 3D finite element analysis is conducted, and the numerical model is validated against the test results

Applications of Finite Element Modeling for Mechanical and Mechatronic Systems

Modern engineering practice requires advanced numerical modeling because, among other things, it reduces the costs associated with prototyping or predicting the occurrence of potentially dangerous situations during operation in certain defined conditions. Thus far, different methods have been used to implement the real structure into the numerical version. The most popular uses have been variations of the finite element method (FEM). The aim of this Special Issue has been to familiarize the reader with the latest applications of the FEM for the modeling and analysis of diverse mechanical problems. Authors are encouraged to provide a concise description of the specific application or a potential application of the Special Issue