We study the question of approximability for the inverse of the FEM stiffness matrix for (scalar) second order elliptic boundary value problems by blockwise low rank matrices such as those given by the H-matrix format introduced by Hackbusch (Computing 62(2):89–108, 1999). We show that exponential convergence in the local block rank r can be achieved. We also show that exponentially accurate LU...

Marinković A, Mih JD, Park J-A, Liu F, Tschumperlin DJ. Improved throughput traction microscopy reveals pivotal role for matrix stiffness in fibroblast contractility and TGFresponsiveness. Am J Physiol Lung Cell Mol Physiol 303: L169–L180, 2012. First published June 1, 2012; doi:10.1152/ajplung.00108.2012.—Lung fibroblast functions such as matrix remodeling and activation of latent transforming...

Deployable trusses that are widely applied in space missions utilize many hinged members to adapt to different geometrical shapes and work conditions. This paper presents two improved finite elements for a link and a bending beam to calculate dynamic characteristics of non-jointed and jointed trusses. First, the axial and transverse wave motion equations of a beam are used to get the shape func...

The mechanical properties of the extracellular matrix (ECM) in which cells reside have emerged as an important regulator of cell fate. While materials based on natural ECM have been used to implicate the role of substrate stiffness for cell fate decisions, it is difficult in these matrices to isolate mechanics from other structural parameters. In contrast, fully synthetic hydrogels offer indepe...

This article develops a simple linear model for the motion of a Stewart platform in a stationary position. That is, the situation where the platform is at rest and is then subject to an impulsive disturbance. The hydraulic actuators are modelled as simple spring-dashpot systems and the stiffness and damping matrices of the system are derived. It is found that the damping and stiffness matrices ...

In this paper, free vibrations of large repetitive regular planar and space trusses are considered. For this kind of structures the corresponding stiffness and mass matrices have tri-diagonal block and in the canonical form, ) , , ( T F B A B K  and ) , , ( 0 D 0 M G  , which simplifies their Eigen frequencies. Practical large space and planar trusses contains with repetitive units, known as ...

Finding efficient and physically based methods to interactively simulate deformable objects is a challenging issue. The most promising methods addressing this issue are based on finite elements and multigrid solvers. However, these multigrid methods still suffer, when used to simulate large deformations, from two pitfalls, depending on the kind of grids hierarchy used. If embedded grids are use...

The physical properties of two-dimensional (2D) extracellular matrices (ECMs) modulate cell adhesion dynamics and motility, but little is known about the roles of local microenvironmental differences in three-dimensional (3D) ECMs. Here we generate 3D collagen gels of varying matrix microarchitectures to characterize their regulation of 3D adhesion dynamics and cell migration. ECMs containing b...

Significant progress has been achieved toward elucidating the molecular mechanisms that underlie breast cancer progression; yet, much less is known about the associated cellular biophysical traits. To this end, we use time-lapsed confocal microscopy to investigate the interplay among cell motility, three-dimensional (3D) matrix stiffness, matrix architecture, and transforming potential in a mam...

Finite element model correction of quadratic eigenvalue problems (QEPs) using a symmetric eigenstructure assignment technique was proposed by Zimmerman and Widengren (Zimmerman, D., and Widengren, M., “Correcting Finite Element Models Using a Symmetric Eigenstructure Assignment Technique,” AIAA Journal, Vol. 28, No. 9, 1990, pp. 1670–1676) and incorporates the measured model data into the finit...