Comparing structures of stiffness matrices using invariants

2005 ◽  
pp. 85-92 ◽  
Author(s):  
Michael Griffis ◽  
Joseph Duffy
Keyword(s):  
Stiffness Matrices

Schur complement spectral bounds for large hybrid FETI-DP clusters and huge three-dimensional scalar problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zdeněk Dostál ◽  
Tomáš Brzobohatý ◽  
Oldřich Vlach
Keyword(s):  
Condition Number ◽  
Three Dimensional ◽  
Schur Complement ◽  
Decomposition Methods ◽  
Stiffness Matrices ◽  
Spectral Bounds ◽  
Schur Complements ◽  
Linear Problems ◽  
Primal Method ◽  
Large Clusters

Abstract Bounds on the spectrum of Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients of the convergence analysis of FETI (finite element tearing and interconnecting) based domain decomposition methods. Here we give bounds on the regular condition number of Schur complements of “floating” clusters arising from the discretization of 3D Laplacian on a cube decomposed into cube subdomains. The results show that the condition number of the cluster defined on a fixed domain decomposed into m × m × m cube subdomains connected by face and optionally edge averages increases proportionally to m. The estimates support scalability of unpreconditioned H-FETI-DP (hybrid FETI dual-primal) method. Though the research is most important for the solution of variational inequalities, the results of numerical experiments indicate that unpreconditioned H-FETI-DP with large clusters can be useful also for the solution of huge linear problems.

Direct stiffness matrices of BEs in the Galerkin BEM formulation

2001 ◽  
Vol 20 (2) ◽  
pp. 277-298 ◽  
Author(s):  
T. Panzeca ◽  
H. Fujita Yashima ◽  
M. Salerno
Keyword(s):  
Stiffness Matrices ◽  
Direct Stiffness

Analytical Simulation of Dynamically Equivalent Components

1986 ◽  
Vol 108 (4) ◽  
pp. 394-400
Author(s):  
Z. N. Ibrahim
Keyword(s):  
Dynamic Characteristic ◽  
Dynamic Model ◽  
Single Degree Of Freedom ◽  
Residual Mass ◽  
Single Degree ◽  
Modal Synthesis ◽  
Stiffness Matrices ◽  
Analytical Simulation ◽  
Modal Mass ◽  
Residual Stiffness

The inertia concept of modal mass was developed to provide a consistent methodology for establishing an analytically equivalent dynamic model of any discrete section within a complex piping network. The multidegree of freedom system is reduced to several multiple excitation single degree of freedom (SDOF) systems representing its modal masses and modal stiffnesses. The multiple excitation residual mass and residual stiffness matrices were also formulated. The combination of modal mass-modal stiffness SDOF systems and residual mass-residual stiffness matrices can simulate the complete dynamic characteristic of any desired portion of the piping network. This technique was extended to cover substructuring applications, and was proved mathematically to be equivalent to the conventional modal synthesis formulation.

Three-Dimensional Parametric Finite-Volume Homogenization of Periodic Materials with Multi-Scale Structural Applications

2018 ◽  
Vol 10 (04) ◽  
pp. 1850045 ◽  
Author(s):  
Qiang Chen ◽  
Guannan Wang ◽  
Xuefeng Chen
Keyword(s):  
Finite Volume ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Attractive Alternative ◽  
Matrix Assembly ◽  
Functionally Graded Composite ◽  
Multi Scale ◽  
Hexahedral Elements ◽  
Stiffness Matrices ◽  
Structural Applications

In order to satisfy the increasing computational demands of micromechanics, the Finite-Volume Direct Averaging Micromechanics (FVDAM) theory is developed in three-dimensional (3D) domain to simulate the multiphase heterogeneous materials whose microstructures are distributed periodically in the space. Parametric mapping, which endorses arbitrarily shaped and oriented hexahedral elements in the microstructure discretization, is employed in the unit cell solution. Unlike the finite-element (FE) technique, the expressions for local stiffness matrices are derived explicitly, enabling efficient global stiffness matrix assembly using an easily implementable algorithm. To demonstrate the accuracy and efficiency of the proposed theory, the homogenized moduli and localized stress distributions produced by the FE analyses are given for comparisons, where excellent agreement is always obtained for the 3D microstructures with different geometrical and material properties. Finally, a multi-scale stress analysis of functionally graded composite cylinders is conducted. This extension further increases the FVDAM’s range of applicability and opens new opportunities for pursuing other areas, providing an attractive alternative to the FE-based approaches that may be compared.

scholarly journals An Effective Method of Modeling the Deformation Behavior of Polymer Sandwich Structures with Adhesive Joints

2021 ◽  
Author(s):  
László Takács ◽  
Ferenc Szabó
Keyword(s):  
Deformation Behavior ◽  
Sandwich Structures ◽  
Experimental Tests ◽  
Mechanical Tests ◽  
Adhesive Joints ◽  
Core Material ◽  
Full Vehicle ◽  
Novel Approach ◽  
Stiffness Matrices ◽  
Layered Shells

AbstractPolymer sandwich structures have high bending stiffness and strength and also low weight. Therefore, they are widely used in the transportation industry. In the conceptual design phase, it is essential to have a method to model the mechanical behavior of the sandwich and its adhesive joints accurately in full-vehicle scale to investigate different structure partitioning strategies. In this paper, a novel approach using finite element modeling is introduced. The sandwich panels are modeled with layered shells and the joint lines with general stiffness matrices. Stiffness parameters of the face-sheets and the core material are obtained via mechanical tests. Stiffness parameters of the joints are determined by using the method of Design of Experiments, where detailed sub-models of the joints serve as a reference. These models are validated with experimental tests of glass-fiber reinforced vinyl ester matrix composite sandwich structure with a foam core. By using two joint designs and three reference geometries, it is shown that the method is suitable to describe the deformation behavior in a full-vehicle scale with sufficient accuracy.

Ill-Conditioned Stiffness Matrices

1966 ◽  
Vol 92 (6) ◽  
pp. 443-457
Author(s):  
Jayant M. Shah
Keyword(s):  
Stiffness Matrices
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