scholarly journals NURBS-Enhanced Meshfree Method with an Integration Subtraction Technique for Complex Topology

2020 ◽  
Vol 10 (7) ◽  
pp. 2587 ◽  
Author(s):  
Yunzhen Liu ◽  
Zhiqiang Wan ◽  
Chao Yang ◽  
Xiaozhe Wang
Keyword(s):  
Computer Aided Design ◽  
Interpolation Method ◽  
Meshfree Method ◽  
Subtraction Technique ◽  
Good Efficiency ◽  
Linear Elastic ◽  
Complex Topology ◽  
Point Interpolation Method ◽  
Meshfree Analysis ◽  
Aided Design

In this paper, we present an integration subtraction technique to model holes interactively in a predesigned domain for adaptive problems. This technique involves two approaches, the normal subtraction technique and the moving subtraction technique. In the basic normal subtraction technique, the predesigned domain can be meshed using any methods as an initial integration background cell for meshfree analysis. Holes are described using closed non-uniform rational B-spline (NURBS) curves to preserve the exact computer-aided design (CAD) geometry and are meshed alone using the homotopic method, so they can easily be subtracted from the predesigned domain with no refinement. On the other hand, when the hole size is varying, the moving subtraction technique, in which only the changing part between the new and old boundaries needs to be integrated and subtracted, is more efficient. Compared with the standard radial point interpolation method (RPIM) and finite element method (FEM) in three linear elastic examples with different holes, the excellent accuracy and good efficiency of the proposed method are demonstrated, and its feasibility in complex topology problems is verified.

Towards Computer Aided Design and Analysis of Spatial Flexure Mechanisms

2016 ◽  
Author(s):  
Omer Anil Turkkan ◽  
Hai-Jun Su
Keyword(s):  
Computer Aided Design ◽  
Screw Theory ◽  
Design Tool ◽  
Future Design ◽  
Linear Elastic ◽  
Wide Range ◽  
Speed Up ◽  
System Equations ◽  
Compliance Matrices ◽  
Aided Design

Flexure mechanisms are the central part of numerous precision instruments and devices that are used in a wide range of science and engineering applications and currently, design of flexure mechanisms often heavily relies on designers’ previous hands-on experience. Therefore, a design tool that will speed up the design process is needed and this paper will introduce a systematic approach for building the necessary equations that are based on screw theory and linear elastic theory to analyze flexure mechanisms. A digital library of commonly used flexure elements must be available for a design tool and therefore, we first present the compliance matrices of commonly used flexure components. Motion twists and force wrenches of the screw theory can be related with these compliance matrices. Then, we introduce an algorithm that constructs the required linear system equations from individual compliance equations. This algorithm is applicable to flexure mechanisms with serial, parallel or hybrid chains. Finally, the algorithm is tested with a flexure mechanisms and it is shown that this approach can be the core of a future design tool.

Meshfree Method Analysis of Biot's Consolidation Using Cell-Based Smoothed Point Interpolation Method

2016 ◽  
Vol 846 ◽  
pp. 409-414
Author(s):  
Arash Tootoonchi ◽  
Arman Khoshghalb ◽  
Nasser Khalili
Keyword(s):  
Interpolation Method ◽  
Meshfree Method ◽  
Delta Function ◽  
Shape Functions ◽  
Point Interpolation Method ◽  
Background Mesh ◽  
Point Interpolation ◽  
Support Domain ◽  
Biot’S Equations ◽  
Method Analysis

A set of cell-based smoothed point interpolation methods are proposed for the numerical analysis of Biot’s formulation. In the proposed methods, the problem domain is discretized using a triangular background mesh. Shape functions are constructed using either polynomial or radial point interpolation method (PIM), leading to the delta function property of shape functions and consequently, easy implementation of essential boundary conditions. The Biot’s equations are discretised in space and time. A variety of support domain selection schemes (T-schemes) are investigated. The accuracy and convergence rate of the proposed methods are examined by comparing the numerical results with the analytical solution for the benchmark problem of one dimensional consolidation.

scholarly journals Analysis of calculations when creating a theoretical drawing of a tug by the interpolation method

2021 ◽  
pp. 24-32
Author(s):  
Svetlana V. Davydova ◽  
Ivan V. Andriyanov Andriyanov
Keyword(s):  
Computer Aided Design ◽  
Software Package ◽  
Interpolation Method ◽  
Transformation Method ◽  
Design Work ◽  
Manual Methods ◽  
Modular Method ◽  
Aided Design ◽  
Design And Methods ◽  
Classical Interpolation

The development of a theoretical drawing by manual methods is notable for considerable laboriousness, in this regard, the use of methods that significantly reduce the development time and increase its quality is relevant. In this work, a comparative analysis of methods for obtaining ordinates of a theoretical drawing is carried out. The existing methods of computer-aided design and methods of forming a theoretical drawing are considered: classical, interpolation, affine transformation method, modular method. The process of development of the surface of the tug by the interpolation method is shown, the substantiation of its application is carried out. On the basis of the developed model, a program for calculating the ordinates of the theoretical drawing of tugboats was developed. The results of the software package operation are presented, namely, the ordinates of the theoretical drawing of the tugboat and the hull of the theoretical drawing, as well as the analysis of the calculation accuracy. The adopted approach to the development of the ship's surface can significantly reduce the time and cost of design work on the development of the ship's surface, can be used for its further automation and use as scientific, industrial and educational purposes.

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