This paper considers the hp-finite element discretization of an elliptic boundary value problem using tetrahedral elements. The discretization uses a polynomial basis in which the number of nonzero entries per row is bounded independently of the polynomial degree. The authors present an algorithm which computes the nonzero entries of the stiffness matrix in optimal complexity. The algorithm is ...

In order to calculate the equivalent torsional-warping stiffness of Reinforced Concrete (RC) cores that have thin-walled open cross-section, a new analytical methodology, which combines Vlasov torsion theory with Bernoulli bending theory, is presented herein. As basis calculations, we use principal elastic reference system core from this consider known. Furthermore, start point core's exact sec...

Unit cell homogenization techniques are applied on multiple length scales to compute the macroscopic hyperelastic stiffness characteristics of textile-reinforced polymer matrix composites. On the smallest scale (~50μm) the effective transversely isotropic properties of tows (or yarns) are computed based on both fiber and matrix properties. These position-dependent transversely isotropic effecti...

Stem cells regulate their fate by binding to, and contracting against, the extracellular matrix. Recently, it has been proposed that in addition to matrix stiffness and ligand type, the degree of coupling of fibrous protein to the surface of the underlying substrate, that is, tethering and matrix porosity, also regulates stem cell differentiation. By modulating substrate porosity without alteri...

Neural progenitor cell (NPC) culture within three-dimensional (3D) hydrogels is an attractive strategy for expanding a therapeutically relevant number of stem cells. However, relatively little is known about how 3D material properties such as stiffness and degradability affect the maintenance of NPC stemness in the absence of differentiation factors. Over a physiologically relevant range of sti...

we give a new recursive method to compute the number of cliques and cycles of a graph. this method is related, respectively to the number of disjoint cliques in the complement graph and to the sum of permanent function over all principal minors of the adjacency matrix of the graph. in particular, let $g$ be a graph and let $overline {g}$ be its complement, then given the chromatic polynomial of...

In order to investigate the influence of the stiffness of the compliant prismatic pair, a planar four-bar parallelogram, in a fully compliant parallel mechanism, the stiffness model of the passive compliant prismatic pair in a compliant parallel positioning stage is established using the compliant matrix method and matrix transformation. The influences of the constraints and the compliance of t...

In order to investigate the influence of the stiffness of the compliant prismatic pair, a planar four-bar parallelogram, in a fully compliant parallel mechanism, the stiffness model of the passive compliant prismatic pair in a compliant parallel positioning stage is established using the compliant matrix method and matrix transformation. The influences of the constraints and the compliance of t...