Definition of ANCF Finite Elements

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Ahmed A. Shabana
Keyword(s):  
Finite Elements ◽  
Computer Aided Design ◽  
Displacement Vector ◽  
Solution Procedure ◽  
Position Vector ◽  
Algebraic Equations ◽  
Nodal Coordinates ◽  
Definition Of ◽  
Isoparametric Finite Elements ◽  
Aided Design

Since the absolute nodal coordinate formulation (ANCF) was introduced, a large number of fully parametrized and gradient deficient finite elements were developed. Some of the finite elements (FE) proposed do not fall into the ANCF category, and for this reason, this technical brief describes the general requirements for ANCF finite elements. As discussed in this paper, some of the conventional isoparametric finite elements can describe arbitrary rigid body displacements and can be used with a nonincremental solution procedure. Nonetheless, these isoparametric elements, particularly the ones that employ position coordinates only, are of the C0 type and do not ensure the continuity of the position vector gradients. It is also shown that the position vector gradient continuity conditions can be described using homogeneous algebraic equations, and such conditions are different from those conditions that govern the displacement vector gradients. The use of the displacement vector gradients as nodal coordinates does not allow for an isoparametric representation that accounts for both the initial geometry and displacements using one kinematic description, can make the element assembly more difficult, and can complicate imposing linear algebraic constraint equations at a preprocessing stage. Understanding the ANCF geometric description will allow for the development of new mechanics-based computer-aided design (CAD)/analysis systems as briefly discussed in this paper.

Convergence Characteristics of Geometrically Accurate Spatial Finite Elements

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
Brian Tinsley ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Elements ◽  
Computer Aided Design ◽  
Eigenvalue Analysis ◽  
Reference Configuration ◽  
Position Vector ◽  
B Spline ◽  
Split Method ◽  
Stiffness Matrices ◽  
General Continuum ◽  
Aided Design

Abstract The convergence characteristics of three geometrically accurate spatial finite elements (FEs) are examined in this study using an eigenvalue analysis. The spatial beam, plate, and solid elements considered in this investigation are suited for both structural and multibody system (MBS) applications. These spatial elements are based on geometry derived from the kinematic description of the absolute nodal coordinate formulation (ANCF). In order to allow for an accurate reference-configuration geometry description, the element shape functions are formulated using constant geometry coefficients defined using the position-vector gradients in the reference configuration. The change in the position-vector gradients is used to define a velocity transformation matrix that leads to constant element inertia and stiffness matrices in the case of infinitesimal rotations. In contrast to conventional structural finite elements, the elements considered in this study can be used to describe the initial geometry with the same degree of accuracy as B-spline and nonuniform rational B-spline (NURBS) representations, widely used in the computer-aided design (CAD). An eigenvalue analysis is performed to evaluate the element convergence characteristics in the case of different geometries, including straight, tapered, and curved configurations. The frequencies obtained are compared with those obtained using a commercial FE software and analytical solutions. The stiffness matrix is obtained using both the general continuum mechanics (GCM) approach and the newly proposed strain split method (SSM) in order to investigate its effectiveness as a locking alleviation technique.

Computer-Aided Design Synthesis Using Syntactic Solid Modeling

1994 ◽  
Author(s):  
Vassilios E. Theodoracatos ◽  
Xiaogang Guan
Keyword(s):  
Computer Aided Design ◽  
Solid Modeling ◽  
Large Set ◽  
Complex Structures ◽  
Design Synthesis ◽  
Computer Aided ◽  
Grammar Rules ◽  
Small Set ◽  
Definition Of ◽  
Aided Design

Abstract This paper presents a new Computer-Aided Design (CAD) synthesis model which uses Plex Grammar as structural relationship descriptors and NURBS surface representation for constructing standard and non-standard solid entities. Here, the designer uses a syntactic design methodology for early topological and geometrical definition of the structure of concept alternatives resulting from the design process. This syntactic scheme provides the capability of describing a large set of complex structures by using a small set of simple entities. The recursive nature of the grammar and the hierarchical representation of the structure makes the description of complex structures simple and under the direct control of the designer. An object structure constructive tree is generated and subsequently translated into Plex Grammar production rules in order to form an Interconnection Matrix (ICM) expressing. The resulting Plex structure defined in the ICM expresses the topological information among entities which form the specific types of objects. By modifying the Plex grammar rules, various objects with different geometry and topology can easily be reconstructed. Compared to conventional solid modeling techniques, this approach provides more systematic object generation, easy manipulation and modification, control over congruity and the ability to represent sculptured shapes. Several examples of syntactic solid modeling applied in design synthesis will be presented for further usage in downstream applications.

A Dual Environment for 3D Modeling With User-Defined Free Form Features

2007 ◽  
Author(s):  
Thomas R. Langerak ◽  
Joris S. M. Vergeest
Keyword(s):  
Computer Aided Design ◽  
Shape Representation ◽  
Target Surface ◽  
Free Form ◽  
Dynamic Feature ◽  
Cad Models ◽  
Form Features ◽  
Definition Of ◽  
High Level ◽  
Aided Design

Modeling with free form features has become the standard in Computer-Aided Design (CAD). With the increasing complexity of free form CAD models, features offer a high-level approach to modeling shapes. However, in most commercial modeling packages, only a static set of free form features is available. Researchers have tried to solve this problem by coming up with methods for user-driven free form feature definition, but failed to connect their methods to a means to instantiate these user-driven free form features on a target surface. Reversely, researchers have proposed tools for modeling with free form features, but these methods are time-intensive in that they are as of yet unsuitable for pre-defined features. This paper presents a new method for user-driven feature definition, as well as a method to instantiate these user-defined features on a target surface. We propose the concept of a dual environment, in which the definition of a feature is maintained simultaneously with its instance on a target surface, allowing the user to modify the definition of an already instantiated feature. This dual environment enables dynamic feature modeling, in which the user is able to change the definition of instantiated features on-the-fly. Furthermore, the proposed instantiation method is independent from the type of shape representation of the target surface and thereby increases the applicability of the method. The paper includes an extensive application example and discusses the results and shortcomings of the proposed methods.

The calculation of gear pump porting areas by mathematical means

2014 ◽  
Vol 229 (1) ◽  
pp. 180-188 ◽  
Author(s):  
Martin K Yates
Keyword(s):  
Computer Aided Design ◽  
Gear Pump ◽  
Fuel Delivery ◽  
Lumped Parameter ◽  
Pinion Gear ◽  
Computer Aided ◽  
Gear Pumps ◽  
Aero Engines ◽  
Definition Of ◽  
Aided Design

Twin pinion gear pumps are used widely in industrial hydraulics and as fuel-delivery pumps for aero engines. The kinematics of the pumping action leads to high-flow rates into and out of the meshing gears, and at the high speeds used with aerospace fuel pumps cavitation can occur. One-dimensional ‘lumped parameter’ models are often used to analyse this type of pump. These methods rely on an accurate description of the volume trapped by the meshing teeth and the flow areas during the meshing cycle. Typically, multiple computer-aided design models have to be created to calculate these values during the meshing cycle. This paper presents a mathematical method for calculating these parameters based on a parametric definition of the gear and inlet and outlet porting. Green's theorem is used to allow line integrals around the periphery of the tooth spaces to be used to calculate the volumes and flow areas. Winding numbers are used to calculate the inflow and outflow areas that are formed by the intersection of the trapped volume and the side area porting. The method is validated against computer-aided design model data. This method is well suited for incorporation in an optimisation algorithm since the geometry is defined parametrically.

A Dual Environment for 3D Modeling With User-Defined Freeform Features

2009 ◽  
Vol 9 (2) ◽  
Author(s):  
Thomas R. Langerak ◽  
Joris S. M. Vergeest
Keyword(s):  
3D Modeling ◽  
Computer Aided Design ◽  
Target Surface ◽  
Feature Modeling ◽  
Dynamic Feature ◽  
Design Features ◽  
Computer Aided ◽  
Definition Of ◽  
High Level ◽  
Aided Design

Modeling with freeform features has become the standard in computer-aided design. Features offer a high-level approach to modeling shapes. However, in most commercial modeling packages, only a static set of freeform features is available. A new method for user-driven feature definition is presented, as well as a method to instantiate these user-defined features on a target surface. We propose the concept of a dual environment, in which the definition of a feature is maintained parallel to its instance on a target surface. This dual environment enables dynamic feature modeling, in which the user is able to change the definition of instantiated features on-the-fly.

Automatic Determination of Feature Interactions in Design-for-Manufacturing Analysis

1995 ◽  
Vol 117 (1) ◽  
pp. 2-9 ◽  
Author(s):  
R. Gadh ◽  
F. B. Prinz
Keyword(s):  
Computer Aided Design ◽  
Boundary Representation ◽  
Abstract Entity ◽  
Automatic Determination ◽  
New Approach ◽  
Feature Interactions ◽  
Definition Of ◽  
High Level ◽  
Aided Design

The current paper discusses a fundamentally new approach to defining and finding interactions in computer-aided design (CAD) forms or features. Feature classes are defined using a high-level abstract entity called a loop. Loops define features in a general manner and aid in the definition of feature boundaries as well. Interactions between features exist due to interactions between their boundaries. Several types of interactions are defined and automatically determined from the boundary representation solid model of the part subsequent to performing feature extraction.

scholarly journals Novel Procedure for Designing and 3D Printing a Customized Surgical Template for Arthrodesis Surgery on the Sacrum

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 334 ◽  
Author(s):  
Francesco Naddeo ◽  
Alessandro Naddeo ◽  
Nicola Cappetti ◽  
Emilio Cataldo ◽  
Riccardo Militio
Keyword(s):  
3D Printing ◽  
Computer Aided Design ◽  
Standard Procedure ◽  
Anatomical Landmarks ◽  
X Rays ◽  
Surgical Template ◽  
3D Printed ◽  
Definition Of ◽  
Aided Design

In this article, the authors propose a novel procedure for designing a customized 3D-printed surgical template to guide surgeons in inserting screws into the sacral zone during arthrodesis surgeries. The template is characterized by two cylindrical guides defined by means of trajectories identified, based on standard procedure, via an appropriate Computer-Aided-Design (CAD)-based procedure. The procedure is based on the definition of the insertion direction by means of anatomical landmarks that enable the screws to take advantage of the maximum available bone path. After 3D printing, the template adheres perfectly to the bone surface, showing univocal positioning by exploiting the foramina of the sacrum, great maneuverability due to the presence of an ergonomic handle, as well as a break system for the two independent guides. These features make the product innovative. Thanks to its small size and the easy anchoring, the surgeon can simply position the template on the insertion area and directly insert the screws, without alterations to standard surgical procedures. This has the effect of reducing the overall duration of the surgery and the patient’s exposure to X-rays, and increasing both the safety of the intervention and the quality of the results.

Ideal Compliant Joints and Integration of Computer Aided Design and Analysis

2014 ◽  
Author(s):  
Ashraf M. Hamed ◽  
Paramsothy Jayakumar ◽  
Michael D. Letherwood ◽  
David J. Gorsich ◽  
Antonio M. Recuero ◽  
...  
Keyword(s):  
Computer Aided Design ◽  
Large Scale ◽  
Algebraic Equations ◽  
B Spline ◽  
Constraint Equations ◽  
Compliant Joints ◽  
Linear Algebraic Equations ◽  
Dependent Variables ◽  
Computer Aided ◽  
Aided Design

This paper discusses fundamental issues related to the integration of computer aided design and analysis (I-CAD-A) by introducing a new class of ideal compliant joints that account for the distributed inertia and elasticity. The absolute nodal coordinate formulation (ANCF) degrees of freedom are used in order to capture modes of deformation that cannot be captured using existing formulations. The ideal compliant joints developed can be formulated, for the most part, using linear algebraic equations, allowing for the elimination of the dependent variables at a preprocessing stage, thereby significantly reducing the problem dimension and array storage needed. Furthermore, the constraint equations are automatically satisfied at the position, velocity, and acceleration levels. When using the proposed approach to model large scale chain systems, differences in computational efficiency between the augmented formulation and the recursive methods are eliminated, and the CPU times resulting from the use of the two formulations become similar regardless of the complexity of the system. The elimination of the joint constraint equations and the associated dependent variables also contribute to the solution of a fundamental singularity problem encountered in the analysis of closed loop chains and mechanisms by eliminating the need to repeatedly change the chain or mechanism independent coordinates. It is shown that the concept of the knot multiplicity used in computational geometry methods, such as B-spline and NURBS (Non-Uniform Rational B-Spline), to control the degree of continuity at the breakpoints is not suited for the formulation of many ideal compliant joints. As explained in this paper, this issue is closely related to the inability of B-spline and NURBS to model structural discontinuities. Another contribution of this paper is demonstrating that large deformation ANCF finite elements can be effective, in some MBS application, in solving small deformation problems. This is demonstrated using a heavily constrained tracked vehicle with flexible link chains. Without using the proposed approach, modeling such a complex system with flexible links can be very challenging. The analysis presented in this paper also demonstrates that adding significant model details does not necessarily imply increasing the complexity of the MBS algorithm.

scholarly journals Technological heredity at quality formation of parts manufactured

2018 ◽  
Vol 2018 (10) ◽  
pp. 27-32 ◽  
Author(s):  
Владимир Аверченков ◽  
Vladimir Averchenkov ◽  
Андрей Васильев ◽  
Andrey Vasilev ◽  
М. Хейфец ◽  
...  
Keyword(s):  
Computer Aided Design ◽  
Computer Aided ◽  
Technological Heredity ◽  
Definition Of ◽  
Aided Design ◽  
Quality Formation

The problems of a technological heredity impact upon quality formation and machinery operation properties are considered. The significance of the definition of quantitative dependences taking into account technological heredity manifestation is shown. Simulators for the computer-aided design of engineering ensuring parts quality required are offered.

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