A simple and efficient method for introducing faults into finite element computations

1981 ◽  
Vol 71 (5) ◽  
pp. 1391-1400
Author(s):  
H. J. Melosh ◽  
A. Raefsky
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Displacement Discontinuity ◽  
Element Level ◽  
Single Node ◽  
Node Point ◽  
Local Element ◽  
Great Utility ◽  
Load Vector

abstract This paper outlines a new method, the “split node technique” for introducing fault displacements into finite element numerical computations. The value of the displacement at a single node point shared between two elements depends upon which element it is referred to, thus introducing a displacement discontinuity between the two elements. We show that the modification induced by this splitting can be contained in the load vector, so that the stiffness matrix is not altered. The number of degrees of freedom is not increased by splitting. This method can be implemented entirely on the local element level, and we show rigorously that no net forces or moments are induced on the finite element grid when isoparametric elements are used. This method is thus of great utility in many geological and engineering applications.

A Complaint Mechanism with Freedom Degrees of One Movement and Two Rotations

2014 ◽  
Vol 551 ◽  
pp. 444-447
Author(s):  
Sheng Lin ◽  
Xi Kong ◽  
Chun Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Element Model ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Compliant Mechanism ◽  
Element Model ◽  
Theory Analysis ◽  
The Finite Element Model

Based on the method of Freedom and Constraint Topology (FACT), a compliant mechanism with 3 degrees of freedom is designed. The 3 DOF are one movement and two rotations, which belongs to Case 3, Type 2. The whole stiffness matrix of the compliant mechanism is obtained. The finite element model is established for statics analysis. The results of theory analysis and finite element method are closed.

A Four-Node Tetrahedral Finite Element Based on Space Fiber Rotation Concept

2019 ◽  
Vol 11 (1) ◽  
pp. 67-78
Author(s):  
Kamel Meftah ◽  
Lakhdar Sedira
Keyword(s):  
Finite Element ◽  
Strain Field ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Field Tensor ◽  
Tetrahedral Element ◽  
Numerical Studies ◽  
Rotational Degrees Of Freedom ◽  
Tensor Approximation

Abstract The paper presents a four-node tetrahedral solid finite element SFR4 with rotational degrees of freedom (DOFs) based on the Space Fiber Rotation (SFR) concept for modeling three-dimensional solid structures. This SFR concept is based on the idea that a 3D virtual fiber, after a spatial rotation, introduces an enhancement of the strain field tensor approximation. Full numerical integration is used to evaluate the element stiffness matrix. To demonstrate the efficiency and accuracy of the developed four-node tetrahedron solid element and to compare its performance with the classical four-node tetrahedral element, extensive numerical studies are presented.

A NOVEL TRIANGULAR FINITE ELEMENT PARTITION METHOD FOR FRACTURE SIMULATION WITHOUT ENRICHMENT OF INTERPOLATION

2013 ◽  
Vol 10 (04) ◽  
pp. 1350015 ◽  
Author(s):  
ZHENNAN ZHANG ◽  
DEYONG WANG ◽  
XIURUN GE
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Interpolation Method ◽  
Equation System ◽  
Least Square ◽  
Displacement Discontinuity ◽  
Quadrilateral Element ◽  
Triangular Finite Element ◽  
Fracture Simulation ◽  
Partition Method

A novel 3-node triangular finite element partition method is proposed for fracture simulation. By this method, the crack is directly embedded into the element without any enrichment of interpolation, avoiding the treatment of displacement discontinuity and remeshing. Thus, no extra degrees of freedom are introduced into the equation system. It is done by subdividing the cracked element into a sub-triangular and a sub-quadrilateral element. The deformation field of each sub-element is associated with its adjacent nodes at the same side of crack via least square interpolation method. To represent the contact behaviors of crack faces, a sub-joint element is used to join the sub-triangular and sub-quadrilateral element. The final stiffness matrix of the cracked element is obtained by composing the three sub-element stiffness matrixes together. The simulation results suggest that the present method is validated, simple and efficient.

About Inverse Problem in Heat Transfer

2016 ◽  
Vol 823 ◽  
pp. 373-376
Author(s):  
Adrian Sorin Rosca ◽  
Andrei Gheorghe Nanu ◽  
Doina Roşca
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Finite Element ◽  
Temperature Distribution ◽  
Infrared Image ◽  
Thermal Source ◽  
Element Level ◽  
Finite Element Approach ◽  
Load Vector ◽  
Element Approach

The paper presents a method for obtaining the power of thermal source, based on finite element approach, when the temperature distribution is known from an infrared image. The method is solving for the load vector, and extracts the power at element level from this vector.

scholarly journals Substructure Interface Reduction Techniques to Capture Nonlinearities in Bolted Structures

2020 ◽  
Author(s):  
Aabhas Singh ◽  
Matthew S. Allen ◽  
Robert J. Kuether
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Model Updating ◽  
Computational Cost ◽  
Nonlinear Behavior ◽  
Element Model ◽  
System Level ◽  
Contact Interface ◽  
Single Node ◽  
Structural Dynamic

Abstract Structural dynamic finite element models typically use multipoint constraints (MPC) to condense the degrees of freedom (DOF) near bolted joints down to a single node, which can then be joined to neighboring structures with linear springs or nonlinear elements. Scalability becomes an issue when multiple joints are present in a system, because each requires its own model to capture the nonlinear behavior. While this increases the computational cost, the larger problem is that the parameters of the joint models are not known, and so one must solve a nonlinear model updating problem with potentially hundreds of unknown variables to fit the model to measurements. Furthermore, traditional MPC approaches are limited in how the flexibility of the interface is treated (i.e. with rigid bar elements the interface has no flexibility). To resolve this shortcoming, this work presents an alternative approach where the contact interface is reduced to a set of modal DOF which retain the flexibility of the interface and are capable of modeling multiple joints simultaneously. Specifically, system-level characteristic constraint (S-CC) reduction is used to reduce the motion at the contact interface to a small number of shapes. To capture the hysteresis and energy dissipation that is present during microslip of joints, a hysteretic element is applied to a small number of the S-CC Shapes. This method is compared against a traditional MPC method (using rigid bar elements) on a two-dimensional finite element model of a cantilever beam with a single joint near the free end. For all methods, a four-parameter Iwan element is applied to the interface DOF to capture how the amplitude dependent modal frequency and damping change with vibration amplitude.

A New Enriched Finite Element Method with Application to Static Fracture Problems with Internal Fluid Pressure

2015 ◽  
Vol 07 (03) ◽  
pp. 1550037 ◽  
Author(s):  
Zuorong Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Crack Path ◽  
Fluid Pressure ◽  
Displacement Discontinuity ◽  
Internal Fluid ◽  
Static Fracture ◽  
Enriched Finite Element ◽  
Element Technique

A new enriched finite element technique, for modeling crack problems within the framework of the extended finite element method, is presented. In this method, crack nodes with displacement discontinuity degrees of freedom have been defined and used to explicitly describe the crack geometry and deformation. The crack deformation is represented by these displacement discontinuity degrees of freedom which are associated with the crack nodes distributed along the crack path, and the crack path is determined by the coordinates of the crack nodes which are solution dependent. This enables a direct and efficient description of the crack. Moreover, the corresponding work-conjugate variables allow for directly modeling the forces on the crack surfaces. In addition, this formulation provides a convenient way to calculate the internal fluid pressure within the crack and its contribution to the crack deformation as occurs in hydraulically driven fractures. Numerical experiments of several static fracture problems are provided to demonstrate the performance, utility and accuracy of the new enriched finite element technique by comparing the numerical results with analytical solutions available in the literature.

scholarly journals Modelling of fracture problems in quasi-brittle materials by the E-FEM

2018 ◽  
Vol 11 (2) ◽  
pp. 244-254
Author(s):  
C. Z. S. MARASCA ◽  
E. BITTENCOURT ◽  
V. M. R. D. BESSA
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Constitutive Models ◽  
Brittle Materials ◽  
Exponential Model ◽  
Strong Discontinuity ◽  
Element Level ◽  
Strong Discontinuities ◽  
Consistent Formulation

Abstract In this paper a numerical model with strong discontinuities is presented to address fracture problems in quasi-brittle materials. A non-symmetrical statically and kinematically consistent formulation is implemented. The strong discontinuity in the displacement field is represented using the elemental enrichment finite element method (E-FEM). In other words, the strong discontinuity is introduced into the finite element and the additional degrees of freedom are condensed at the element level, allowing the implementation into existing computational codes. Two constitutive models are used to analyze the behavior of the cracked zone, linear and exponential. The exponential model results are closer to those obtained in experimental data and representative numerical simulations than the linear model.

The Finite Element Model Study of the Pre-Twisted Euler Beam

2012 ◽  
Vol 446-449 ◽  
pp. 3615-3618
Author(s):  
Ying Huang ◽  
Chang Hong Chen ◽  
Jian Shan
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Displacement Function ◽  
Interpolation Function ◽  
Euler Beam ◽  
Systematic Analysis ◽  
Element Stiffness Matrix ◽  
Straight Beam

Based on the traditional mechanical model of straight beam, the paper makes a systematic analysis and research on the pre-twisted Euler beam finite element numerical model. The paper uses two-node model of 12 degrees of freedom, axial displacement interpolation function using 2-node Lagrange interpolation function, beam transverse bending displacements (u and υ) still use the cubic displacement, bending with torsion angle displacement function using cubic polynomial displacement function. Firstly, based on the author previous literature on the flexure strain relationship, the paper deduces the element stiffness matrix of the pre-twisted beam. Finally, by calculating the pre-twisted rectangle section beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted Euler beam element stiffness matrix has good accuracy.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

scholarly journals A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft

1994 ◽  
Author(s):  
Wen Zhang ◽  
Wenliang Wang ◽  
Hao Wang ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Equation Of Motion ◽  
Coupled Systems ◽  
The Finite Element Method ◽  
Bladed Disk ◽  
Modal Synthesis ◽  
Element Approach ◽  
Final Equation

A method for dynamic analysis of flexible bladed-disk/shaft coupled systems is presented in this paper. Being independant substructures first, the rigid-disk/shaft and each of the bladed-disk assemblies are analyzed separately in a centrifugal force field by means of the finite element method. Then through a modal synthesis approach the equation of motion for the integral system is derived. In the vibration analysis of the rotating bladed-disk substructure, the geometrically nonlinear deformation is taken into account and the rotationally periodic symmetry is utilized to condense the degrees of freedom into one sector. The final equation of motion for the coupled system involves the degrees of freedom of the shaft and those of only one sector of each of the bladed-disks, thereby reducing the computer storage. Some computational and experimental results are given.

Sign in / Sign up

Export Citation Format

Share Document