Physics-Based Modeling for Heterogeneous Objects

2003 ◽  
Vol 125 (3) ◽  
pp. 416-427 ◽  
Author(s):  
Xiaoping Qian ◽  
Debasish Dutta
Keyword(s):  
Material Properties ◽  
Degrees Of Freedom ◽  
Critical Issue ◽  
Diffusion Problem ◽  
Material Distribution ◽  
B Spline ◽  
Material Heterogeneity ◽  
Model Object ◽  
Heterogeneous Objects ◽  
Spline Representation

Heterogeneous objects are composed of different constituent materials. In these objects, material properties from different constituent materials are synthesized into one part. Therefore, heterogeneous objects can offer new material properties and functionalities. The task of modeling material heterogeneity (composition variation) is a critical issue in the design and fabrication of such heterogeneous objects. Existing methods cannot efficiently model the material heterogeneity due to the lack of an effective mechanism to control the large number of degrees of freedom for the specification of heterogeneous objects. In this research, we provide a new approach for designing heterogeneous objects. The idea is that designers indirectly control the material distribution through the boundary conditions of a virtual diffusion problem in the solid, rather than directly in the native CAD (B-spline) representation for the distribution. We show how the diffusion problem can be solved using the B-spline shape function, with the results mapping directly to a volumetric B-Spline representation of the material distribution. We also extend this method to material property manipulation and time dependent heterogeneous object modeling. Implementation and examples, such as a turbine blade design and prosthesis design, are also presented. They demonstrate that the physics based B-spline modeling method is a convenient, intuitive, and efficient way to model object heterogeneity.

Physics Based B-Spline Heterogeneous Object Modeling

2001 ◽  
Author(s):  
Xiaoping Qian ◽  
Debasish Dutta
Keyword(s):  
Diffusion Process ◽  
Material Properties ◽  
Degrees Of Freedom ◽  
Heterogeneous Material ◽  
Critical Issue ◽  
Material Composition ◽  
B Spline ◽  
Material Heterogeneity ◽  
Heterogeneous Objects ◽  
Modeling Material

Abstract The task of modeling material heterogeneity (composition variation) is a critical issue in the design and fabrication of heterogeneous objects. Existing methods cannot efficiently model the material heterogeneity, due to the formidable size of the degrees of freedom for the specification of heterogeneous objects. In this research, we provide an intuitive way to model the object heterogeneity by using only a few parameters. These parameters carry physical meanings, such as diffusion coefficients in the diffusion process. We use a B-spline representation to model heterogeneous objects and material properties. We use diffusion equations to generate heterogeneous material composition profile. We then use finite element techniques to solve the material composition equations for the diffusion process. Finally we extend this method to the direct manipulation of material properties in heterogeneous objects.

scholarly journals Image interpolation by rational ball cubic B-spline representation and genetic algorithm

2018 ◽  
Vol 57 (2) ◽  
pp. 931-937 ◽  
Author(s):  
Samreen Abbas ◽  
Malik Zawwar Hussain ◽  
Misbah Irshad
Keyword(s):  
Genetic Algorithm ◽  
Image Interpolation ◽  
B Spline ◽  
Spline Representation

scholarly journals Multi-stable composite twisting structure for morphing applications

2012 ◽  
Vol 468 (2141) ◽  
pp. 1230-1251 ◽  
Author(s):  
X. Lachenal ◽  
P. M. Weaver ◽  
S. Daynes
Keyword(s):  
Analytical Model ◽  
Material Properties ◽  
Degrees Of Freedom ◽  
Design Parameters ◽  
Engineering Structures ◽  
The Past ◽  
Wide Range ◽  
Morphing Structure ◽  
Low Mass ◽  
Unstable States

Conventional shape-changing engineering structures use discrete parts articulated around a number of linkages. Each part carries the loads, and the articulations provide the degrees of freedom of the system, leading to heavy and complex mechanisms. Consequently, there has been increased interest in morphing structures over the past decade owing to their potential to combine the conflicting requirements of strength, flexibility and low mass. This article presents a novel type of morphing structure capable of large deformations, simply consisting of two pre-stressed flanges joined to introduce two stable configurations. The bistability is analysed through a simple analytical model, predicting the positions of the stable and unstable states for different design parameters and material properties. Good correlation is found between experimental results, finite-element modelling and predictions from the analytical model for one particular example. A wide range of design parameters and material properties is also analytically investigated, yielding a remarkable structure with zero stiffness along the twisting axis.

A Local Approach for Computing Smooth B-spline Surfaces for Arbitrary Quadrilateral Base Meshes

2021 ◽  
pp. 1-28
Author(s):  
Dennis Mosbach ◽  
Katja Schladitz ◽  
Bernd Hamann ◽  
Hans Hagen
Keyword(s):  
Degrees Of Freedom ◽  
Tangent Plane ◽  
Local Approach ◽  
Approximation Process ◽  
Surface Approximation ◽  
B Spline ◽  
Spline Surfaces ◽  
Continuous Surface ◽  
Normal Vectors ◽  
The Individual

Abstract We present a method for approximating surface data of arbitrary topology by a model of smoothly connected B-spline surfaces. Most of the existing solutions for this problem use constructions with limited degrees of freedom or they address smoothness between surfaces in a post-processing step, often leading to undesirable surface behavior in proximity of the boundaries. Our contribution is the design of a local method for the approximation process. We compute a smooth B-spline surface approximation without imposing restrictions on the topology of a quadrilateral base mesh defining the individual B-spline surfaces, the used B-spline knot vectors, or the number of B-spline control points. Exact tangent plane continuity can generally not be achieved for a set of B-spline surfaces for an arbitrary underlying quadrilateral base mesh. Our method generates a set of B-spline surfaces that lead to a nearly tangent plane continuous surface approximation and is watertight, i.e., continuous. The presented examples demonstrate that we can generate B-spline approximations with differences of normal vectors along shared boundary curves of less than one degree. Our approach can also be adapted to locally utilize other approximation methods leading to higher orders of continuity.

A B-spline-based approach to heterogeneous objects design and analysis

2007 ◽  
Vol 39 (2) ◽  
pp. 95-111 ◽  
Author(s):  
Pinghai Yang ◽  
Xiaoping Qian
Keyword(s):  
B Spline ◽  
Heterogeneous Objects

scholarly journals Trajectory Planning of Manipulator Using Optimization of Uniform B-Spline

1994 ◽  
Vol 6 (6) ◽  
pp. 491-498 ◽  
Author(s):  
Hiroaki Ozaki ◽  
◽  
Hua Chiu ◽  
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Control Points ◽  
State Variables ◽  
B Spline ◽  
Iterative Computation ◽  
Basic Optimization ◽  
Engineering Problems ◽  
Original Objective ◽  
Optimum Solution

A basic optimization algorithm is presented in this paper, in order to obtain the optimum solution of a two-point boundary value variational problem without constraints. The solution is given by a parallel and iterative computation and described as a set of control points of a uniform B-spline. This algorithm can also be applied to solving problems with some constraints, if we introduce an additional component, namely the potential function, corresponding to constraints in the original objective function. The algorithm is very simple and easily applicable to various engineering problems. As an application, trajectory planning of a manipulator with redundant degrees of freedom is considered under the conditions that the end effector path, the smoothness of movement, and the constraints of the control or the state variables are specified. The validity of the algorithm is well confirmed by numerical examples.

B-spline representation

2002 ◽  
pp. 59-75
Author(s):  
Hartmut Prautzsch ◽  
Wolfgang Boehm ◽  
Marco Paluszny
Keyword(s):  
B Spline ◽  
Spline Representation

Numerical Solution of a Wave Propagation Problem Along Plate Structures Based on the Isogeometric Approach

2018 ◽  
Vol 26 (01) ◽  
pp. 1750030 ◽  
Author(s):  
V. Hernández ◽  
J. Estrada ◽  
E. Moreno ◽  
S. Rodríguez ◽  
A. Mansur
Keyword(s):  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Computational Cost ◽  
Dispersion Curves ◽  
Wave Number ◽  
Spline Functions ◽  
Shape Functions ◽  
B Spline ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems

Ultrasonic guided waves propagating along large structures have great potential as a nondestructive evaluation method. In this context, it is very important to obtain the dispersion curves, which depend on the cross-section of the structure. In this paper, we compute dispersion curves along infinite isotropic plate-like structures using the semi-analytical method (SAFEM) with an isogeometric approach based on B-spline functions. The SAFEM method leads to a family of generalized eigenvalue problems depending on the wave number. For a prescribed wave number, the solution of this problem consists of the nodal displacement vector and the frequency of the guided wave. In this work, the results obtained with B-splines shape functions are compared to the numerical SAFEM solution with quadratic Lagrange shape functions. Advantages of the isogeometric approach are highlighted and include the smoothness of the displacement field components and the computational cost of solving the corresponding generalized eigenvalue problems. Finally, we investigate the convergence of Lagrange and B-spline approaches when the number of degrees of freedom grows. The study shows that cubic B-spline functions provide the best solution with the smallest relative errors for a given number of degrees of freedom.

A Local Refinement Technique for B-Spline Finite Element Shell Modeling

2013 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Finite Element ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Element Model ◽  
Complex Structures ◽  
Local Refinement ◽  
B Spline ◽  
Spline Finite Element ◽  
Shell Finite Element

This paper presents a refinement technique for a B2-spline degenerate isoparametric shell finite element model for the analysis of the vibrational behavior of thin and moderately thick-walled structures. Complex structures to be refined are modeled by means of FE B-spline patches assembled with C0 continuity as usual in FE technique. The model refinement was performed by adding, on the domain of the selected patch, a tensorial set of polynomial B-spline functions, defined on local clamped knot vectors, and normalizing all the functions so that the resulting displacement field remain polynomial and continuous overall the domain except on the boundaries of the refined subdomain. A degrees of freedom trasformation, based on the knot-insertion algorthim, is adopted in order to guarantee the C0 continuity of the displacement field on the boundaries of the refined subdomain. Two numerical examples are presented in order to test the proposed approach. The natural frequencies of two structures, computed by means of the proposed modelling technique, are compared with reference results available in the literature or computed by means of reference standard FE models. Strengths and limits of the approach are finally discussed.

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