Parallelization of Closed-Form Stiffness Matrix Generation for Tetrahedral Finite Elements

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.

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Closed-Form Matrices for Higher Order Tetrahedral Finite Elements

Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing ◽

10.4203/ccp.91.286 ◽

2009 ◽

Author(s):

S.E. McCaslin ◽

P. Shiakolas ◽

B. Dennis ◽

K.L. Lawrence

Keyword(s):

Finite Elements ◽

Closed Form ◽

Higher Order

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Finite Elements for Curved Sandwich Beams

Aeronautical Quarterly ◽

10.1017/s0001925900008027 ◽

1977 ◽

Vol 28 (2) ◽

pp. 123-141 ◽

Cited By ~ 5

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.

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

International Journal of Computational Science and Engineering ◽

10.1504/ijcse.2018.090439 ◽

2018 ◽

Vol 16 (2) ◽

pp. 173

Author(s):

Juan Carlos Osorio ◽

Miguel Cerrolaza ◽

Maritza Perez

Keyword(s):

Finite Elements ◽

Stiffness Matrix

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A CRITICAL EVALUATION OF VARIOUS NONLINEAR BEAM FINITE ELEMENTS

International Journal of Computational Methods ◽

10.1142/s0219876212500454 ◽

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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