In this work we study in detail the conditions under which the stiffness matrix of a spatial system can be transformed into block-diagonal and diagonal form. That is the existence of a coordinate frame in which the stiffness matrix takes on these simple forms. The consequences of a block-diagonal or diagonal stiffness matrix for the invariants of the system, principal screws, von Mises’ invaria...

The free vibration analysis of the functionally graded cylindrical shell panels  with and without cutout is carried out using the finite element method based on a higher-order shear deformation theory. A higher-order theory is used to properly account for transverse shear deformation. An eight noded degenerated isoparametric shell element with nine degrees of freedom at each node is considered....

<:ontinuous deformable models are generally represented using a grid of control points. The elastic properties are then modeled using the interactions between these points. The formulations based on elasticity theory express these interactions using stiffness matrices. These matrices store the elastic properties of the models and they should be evolved in time according to changing elastic prop...

This article deals with the efficient (approximate) inversion of finite element stiffness matrices of general second-order elliptic operators with L∞-coefficients. It will be shown that the inverse stiffness matrix can be approximated by hierarchical matrices (H-matrices). Furthermore, numerical results will demonstrate that it is possible to compute an approximate inverse with almost linear co...

In this paper, we present a theory for bounding the minimum eigenvalues, maximum eigenvalues, and condition numbers of stiffness matrices arising from the p-version of finite element analysis. Bounds are derived for the eigenvalues and the condition numbers, which are valid for stiffness matrices based on a set of general basis functions that can be used in the p-version. For a set of hierarchi...

Assembling stiffness matrices represents a significant cost in many finite element computations. We address the question of optimizing the evaluation of these matrices. By finding redundant computations, we are able to significantly reduce the cost of building local stiffness matrices for the Laplace operator and for the trilinear form for Navier-Stokes. For the Laplace operator in two space di...

Assembling stiffness matrices represents a significant cost in many finite element computations. We address the question of optimizing the evaluation of these matrices. By finding redundant computations, we are able to significantly reduce the cost of building local stiffness matrices for the Laplace operator and for the trilinear form for Navier-Stokes. For the Laplace operator in two space di...

OBJECTIVE Extensive remodeling of the valve ECM in calcific aortic valve sclerosis alters its mechanical properties, but little is known about the impact of matrix mechanics on the cells within the valve interstitium. In this study, the influence of matrix stiffness in modulating calcification by valve interstitial cells (VICs), and their differentiation to pathological phenotypes was assessed....

it is well-known that dam-reservoir interaction has significant effects on the response of dams to the earthquakes. this phenomenon should be considered more exactly in the seismic design of dams with a rational and reliable dynamic analysis method. in this research, seismic analysis of the dam-reservoir is studied as a wave propagation problem by using legendre spectral element method (sem). t...