A Generalized Conforming Quadrilateral Membrane Element Less Sensitive to Geometric Distortion

1998 ◽  
Vol 1 (3) ◽  
pp. 185-191 ◽  
Author(s):  
Yin Xu ◽  
Zhifei Long ◽  
Yuqiu Long
Keyword(s):  
Finite Element ◽  
High Precision ◽  
Degrees Of Freedom ◽  
Geometric Distortion ◽  
Finite Element Models ◽  
Membrane Element ◽  
Mesh Distortion ◽  
Long Period ◽  
Rotational Degrees Of Freedom ◽  
General Method

Many finite element models have very acceptable performance when the computing meshes are regular. However, as the level of mesh distortion is increasing, the accuracy of the solutions deteriorates rapidly. Therefore, how to formulate an element that is less sensitive to geometric distortion is an important question for study for a long period. In this paper, a simple quadrilateral membrane element with rotational degrees-of-freedom is developed with the approach of the generalized conforming element proposed by Long Yuqiu (1989). The new element exhibits excellent feature, that is, less sensitive to geometric distortion. A general method to formulate high precision finite element less sensitive to geometric distortion is provided in this paper.

Dynamics Analysis of Refrigeration Compressor Based on Finite Element and Experimental Modes

2012 ◽  
Vol 499 ◽  
pp. 238-242
Author(s):  
Li Zhang ◽  
Hong Wu ◽  
Yan Jue Gong ◽  
Shuo Zhang
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Modal Analysis ◽  
Natural Frequency ◽  
High Precision ◽  
3D Model ◽  
Finite Element Models ◽  
Dynamics Analysis ◽  
Response Characteristics ◽  
Dynamic Response Characteristics

Based on the 3D model of refrigeration's compressor by Pro/E software, the analyses of theoretical and experimental mode are carried out in this paper. The results show that the finite element models of compressor have high precision dynamic response characteristics and the natural frequency of the compressor, based on experimental modal analysis, can be accurately obtained, which will contribute to further dynamic designs of mechanical structures.

A Parallel Solution Strategy for Finite Element Models

1996 ◽  
Author(s):  
Jordan J. Cox ◽  
Jeffrey A. Talbert ◽  
Eric Mulkay
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Decomposition Methods ◽  
Finite Element Models ◽  
Unique Contribution ◽  
Matrix Equations ◽  
Parallel Solution ◽  
The Finite Element Model ◽  
Parallel Fashion

Abstract This paper presents a method for naturally decomposing finite element models into sub-models which can be solved in a parallel fashion. The unique contribution of this paper is that the decomposition strategy comes from the geometric features used to construct the solid model that the finite element model represents. Domain composition and domain decomposition methods are used to insure global compatibility. These techniques reduce the N2 behavior of traditional matrix solving techniques, where N is the number of degrees of freedom in the global set of matrix equations, to a sum of m matrices with n2 behavior, where n represents the number of degrees of freedom in the smaller sub-model matrix equations.

Modal Velocity-Based Multiaxial Fatigue Damage Evaluation Using Simplified Finite Element Models

2020 ◽  
Vol 87 (11) ◽  
Author(s):  
Kurthan Kersch ◽  
Elmar Woschke
Keyword(s):  
Finite Element ◽  
Fatigue Damage ◽  
Cross Section ◽  
Multiaxial Fatigue ◽  
Finite Element Models ◽  
Damage Evaluation ◽  
Geometric Factors ◽  
The Relationship ◽  
General Method

Abstract This work proposes a new method for the fatigue damage evaluation of vibrational loads, based on preceding investigations on the relationship between stresses and modal velocities. As a first step, the influence of the geometry on the particular relationship is studied. Therefore, an analytic expression for Euler Bernoulli beams with a non-constant cross section is derived. Afterward, a general method for obtaining geometric factors from finite element (FE) models is proposed. In order to ensure a fast fatigue damage evaluation, strongly simplified FE-models are used for the determination of both factors and measurement locations. The entire method is demonstrated on three mechanical structures and indicates a better compromise between effort and accuracy than existing methods. For all examples, the usage of velocities and geometric factors obtained from simplified FE models enables a sufficient fatigue damage calculation.

Beam Element Structural Dynamics Modification Using Experimental Modal Rotational Data

1995 ◽  
Vol 117 (3A) ◽  
pp. 265-271 ◽  
Author(s):  
John A. Cafeo ◽  
Martin W. Trethewey ◽  
H. Joseph Sommer
Keyword(s):  
Finite Element ◽  
Cantilever Beam ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Structural Dynamic ◽  
Modal Data ◽  
Structural Dynamic Modification ◽  
Dynamic Modification ◽  
Rotational Degrees Of Freedom ◽  
Fixed Beam

Structural dynamic modification (SDM) of a fixed-free (cantilever) beam to convert it into a fixed-fixed beam with experimental modal data is presented. The SDM focuses on incorporating experimental rotational degrees-of-freedom (DOF) measured with a novel laser measurement technique. A cantilever beam is tested to develop the experimental modal database including rotational degrees of freedom. A modal database from a finite-element model also is developed for comparison. A structural dynamic modification, with both databases, is performed using a Bernoulli-Euler beam to ground the free end of the cantilever beam. The hardware is then modified and a second experimental modal analysis of the resulting fixed-fixed beam performed. A finite-element model of the fixed-fixed beam also was created. Comparison of results from these four tests are used to assess the effectiveness of SDM using experimental modal rotational data. The evaluation shows that provided high quality experimental rotational modal data can be acquired, SDM work with beam elements can be effective in yielding accurate results.

scholarly journals Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes

2021 ◽  
Author(s):  
Ivo Steinbrecher ◽  
Alexander Popp ◽  
Christoph Meier
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Lagrange Multiplier ◽  
Degrees Of Freedom ◽  
Element Discretization ◽  
Geometrically Exact Beam ◽  
Coupling Constraints ◽  
Rotational Degrees Of Freedom ◽  
3D Solid ◽  
Cosserat Continua

AbstractThe present article proposes a mortar-type finite element formulation for consistently embedding curved, slender beams into 3D solid volumes. Following the fundamental kinematic assumption of undeformable cross-section s, the beams are identified as 1D Cosserat continua with pointwise six (translational and rotational) degrees of freedom describing the cross-section (centroid) position and orientation. A consistent 1D-3D coupling scheme for this problem type is proposed, requiring to enforce both positional and rotational constraints. Since Boltzmann continua exhibit no inherent rotational degrees of freedom, suitable definitions of orthonormal triads are investigated that are representative for the orientation of material directions within the 3D solid. While the rotation tensor defined by the polar decomposition of the deformation gradient appears as a natural choice and will even be demonstrated to represent these material directions in a $$L_2$$ L 2 -optimal manner, several alternative triad definitions are investigated. Such alternatives potentially allow for a more efficient numerical evaluation. Moreover, objective (i.e. frame-invariant) rotational coupling constraints between beam and solid orientations are formulated and enforced in a variationally consistent manner based on either a penalty potential or a Lagrange multiplier potential. Eventually, finite element discretization of the solid domain, the embedded beams, which are modeled on basis of the geometrically exact beam theory, and the Lagrange multiplier field associated with the coupling constraints results in an embedded mortar-type formulation for rotational and translational constraint enforcement denoted as full beam-to-solid volume coupling (BTS-FULL) scheme. Based on elementary numerical test cases, it is demonstrated that a consistent spatial convergence behavior can be achieved and potential locking effects can be avoided, if the proposed BTS-FULL scheme is combined with a suitable solid triad definition. Eventually, real-life engineering applications are considered to illustrate the importance of consistently coupling both translational and rotational degrees of freedom as well as the upscaling potential of the proposed formulation. This allows the investigation of complex mechanical systems such as fiber-reinforced composite materials, containing a large number of curved, slender fibers with arbitrary orientation embedded in a matrix material.

scholarly journals How to compute invariant manifolds and their reduced dynamics in high-dimensional finite element models

2021 ◽  
Author(s):  
Shobhit Jain ◽  
George Haller
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Invariant Manifolds ◽  
Mechanical Systems ◽  
Forced Response ◽  
High Dimensional ◽  
Nonlinear Phenomena ◽  
Finite Element Models ◽  
Engineering Structures ◽  
Backbone Curves

AbstractInvariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful tools for the computation of forced response curves, backbone curves, detached resonance curves (isolas) via exact reduced-order models. For conservative nonlinear mechanical systems, Lyapunov subcenter manifolds and their reduced dynamics provide a way to identify nonlinear amplitude–frequency relationships in the form of conservative backbone curves. Despite these powerful predictions offered by invariant manifolds, their use has largely been limited to low-dimensional academic examples. This is because several challenges render their computation unfeasible for realistic engineering structures described by finite element models. In this work, we address these computational challenges and develop methods for computing invariant manifolds and their reduced dynamics in very high-dimensional nonlinear systems arising from spatial discretization of the governing partial differential equations. We illustrate our computational algorithms on finite element models of mechanical structures that range from a simple beam containing tens of degrees of freedom to an aircraft wing containing more than a hundred–thousand degrees of freedom.

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.

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