Kinematic analysis of linkages based in finite elements and the geometric stiffness matrix

2008 ◽  
Vol 43 (8) ◽  
pp. 964-983 ◽  
Author(s):  
R. Avilés ◽  
A. Hernández ◽  
E. Amezua ◽  
O. Altuzarra
Keyword(s):  
Finite Elements ◽  
Kinematic Analysis ◽  
Stiffness Matrix ◽  
Geometric Stiffness

Consistent co-rotational framework for Euler-Bernoulli and Timoshenko beam-column elements under distributed member loads

2021 ◽  
pp. 136943322098663
Author(s):  
Yi-Qun Tang ◽  
Wen-Feng Chen ◽  
Yao-Peng Liu ◽  
Siu-Lai Chan
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Traditional Method ◽  
Local Coordinate System ◽  
Frame Structures ◽  
Global Coordinate System ◽  
Single Element ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Geometric Stiffness

Conventional co-rotational formulations for geometrically nonlinear analysis are based on the assumption that the finite element is only subjected to nodal loads and as a result, they are not accurate for the elements under distributed member loads. The magnitude and direction of member loads are treated as constant in the global coordinate system, but they are essentially varying in the local coordinate system for the element undergoing a large rigid body rotation, leading to the change of nodal moments at element ends. Thus, there is a need to improve the co-rotational formulations to allow for the effect. This paper proposes a new consistent co-rotational formulation for both Euler-Bernoulli and Timoshenko two-dimensional beam-column elements subjected to distributed member loads. It is found that the equivalent nodal moments are affected by the element geometric change and consequently contribute to a part of geometric stiffness matrix. From this study, the results of both eigenvalue buckling and second-order direct analyses will be significantly improved. Several examples are used to verify the proposed formulation with comparison of the traditional method, which demonstrate the accuracy and reliability of the proposed method in buckling analysis of frame structures under distributed member loads using a single element per member.

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

2012 ◽  
Vol 28 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. D. Yau ◽  
S.-R. Kuo
Keyword(s):  
Stiffness Matrix ◽  
Virtual Work ◽  
Bending Moment ◽  
Beam Element ◽  
Narrow Beam ◽  
Cross Sectional ◽  
Geometric Stiffness ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

ABSTRACTUsing conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yanget al.'s simplified geometric stiffness matrix [kg]12×12of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.

Brake Squeal Analysis by Finite Elements and Comparisons to Dyno Results

1999 ◽  
Author(s):  
W. V. Nack
Keyword(s):  
Friction Coefficient ◽  
Finite Elements ◽  
Stiffness Matrix ◽  
Approximate Analysis ◽  
Stability Evaluation ◽  
Analysis Method ◽  
Brake Squeal ◽  
Complex Modes ◽  
Baseline Solution ◽  
Test Schedule

Abstract An approximate analysis method for brake squeal is presented. Using MSC/NASTRAN a geometric nonlinear solution is run using a friction stiffness matrix to model the contact between the pad and rotor. The friction coefficient can be pressure dependent. Next, linearized complex modes are found where the interface is set in a slip condition. Since the entire interface is set sliding, it produces the maximum friction work possible during the vibration. It is a conservative measure for stability evaluation. An averaged friction coefficient is measured and used during squeal. Dynamically unstable modes are found during squeal. They are due to friction coupling of neighboring modes. When these modes are decoupled, they are stabilized and squeal is eliminated. Good correlation with experimental results is shown. It will be shown that the complex modes baseline solution is insensitive to the type of variations in pressure and velocity that occur in a test schedule. This is due to the conservative nature of the approximation. Convective mass effects have not been included.

A Study on the Simulation of Flexible Link Mechanics Based on FEM

1997 ◽  
Author(s):  
Koichi Honke ◽  
Yoshio Inoue ◽  
Eiko Hirooka ◽  
Naoki Sugano
Keyword(s):  
Stiffness Matrix ◽  
Large Displacement ◽  
Dynamics Analysis ◽  
Flexible Link ◽  
Finite Rotation ◽  
Fem Model ◽  
Elastic Vibrations ◽  
Link Structure ◽  
Geometric Stiffness ◽  
Inertia Matrix

Abstract The dynamics analysis of link structure, including elastic vibrations, is presented. The two nodes element including large displacement is developed. This element is based on the theory of finite rotation, and includes geometric stiffness. The stiffness matrix and the inertia matrix are obtained from the FEM model by the theory of Guyan’s reduction including large displacement motion. In this paper, we explain the theory of this element and show some examples of analysis.

Finite Elements for Curved Sandwich Beams

1977 ◽  
Vol 28 (2) ◽  
pp. 123-141 ◽  
Author(s):  
P J Holt ◽  
J P H Webber
Keyword(s):  
Finite Elements ◽  
Stiffness Matrix ◽  
Test Cases ◽  
Sandwich Beams ◽  
Honeycomb Core ◽  
The Core ◽  
The Face ◽  
Core Thickness ◽  
Displacement Approach ◽  
Circular Sandwich Ring

SummaryThe formulation of curved finite elements to represent a two-dimensional circular sandwich ring with honeycomb core and laminated faces is investigated. Assumed stress hybrid and equilibrium methods are found to be easier to employ in this case than the displacement approach. Using these methods, an element stiffness matrix is developed. The approximations of membrane faces and an infinite core normal stiffness are then used to develop simpler elements. Test cases show that these assumptions may become invalid, but that they are adequate for most practical cases where the core thickness to radius ratio and the face thickness to core thickness ratio are both low.

Optimising the stiffness matrix integration of n-noded 3D finite elements

2018 ◽  
Vol 16 (2) ◽  
pp. 173
Author(s):  
Juan Carlos Osorio ◽  
Miguel Cerrolaza ◽  
Maritza Perez
Keyword(s):  
Finite Elements ◽  
Stiffness Matrix

A CRITICAL EVALUATION OF VARIOUS NONLINEAR BEAM FINITE ELEMENTS

2012 ◽  
Vol 09 (04) ◽  
pp. 1250045
Author(s):  
A. LAULUSA ◽  
J. N. REDDY
Keyword(s):  
Finite Elements ◽  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Critical Evaluation ◽  
Quadrature Rules ◽  
Nonlinear Beam ◽  
Lagrange Polynomials ◽  
Reduced Integration ◽  
Uniform Interpolation

The characteristics of interdependent interpolation and mixed interpolation nonlinear beam finite elements are investigated in comparison with the equal-order interpolation element with uniform reduced integration. The stiffness matrix of the 3-noded and 4-noded equal order interpolation elements is identical to that of the 2-noded interdependent interpolation element if the internal nodal degrees-of-freedom are eliminated. The extension of the latter to include nonlinear kinematics by approximating the extensional displacement and the twist rotation with quadratic and cubic Lagrange polynomials yields unsatisfactory results. The 2-noded, 3-noded, and 4-noded mixed interpolation elements using one-, two-, and three-point quadrature rules, respectively, are shown to be equivalent to the corresponding uniform interpolation elements employing the same quadrature rules. The equivalence is established in the framework of nonlinear kinematics and anisotropic couplings.

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