An explicit total Lagrangian Fragile Points Method for finite deformation of hyperelastic materials

This research explored a novel explicit total Lagrangian Fragile Points Method (FPM) for finite deformation of hyperelastic materials. In contrast to mesh-based methods, where mesh distortion may pose numerical challenges, meshless methods are more suitable for large deformation modelling since they use enriched shape functions for the approximation of displacements. However, this comes at the expense of extra computational overhead and higher-order quadrature is required to obtain accurate results. In this work, the novel meshless method FPM was used to derive an explicit total Lagrangian algorithm for finite deformation. FPM uses simple one-point integration for exact integration of the Galerkin weak form since it employs simple discontinuous polynomials as trial and test functions, leading to accurate results even with single-point quadrature. The proposed method was evaluated by comparing it with FEM in several case studies considering both the extension and compression of a hyperelastic material. It was demonstrated that FPM maintained good accuracy even for large deformations where FEM failed to converge

RNA activation of haploinsufficient Foxg1 gene in murine neocortex

More than one hundred distinct gene hemizygosities are specifically linked to epilepsy, mental retardation, autism, schizophrenia and neuro-degeneration. Radical repair of these gene deficits via genome engineering is hardly feasible. The same applies to therapeutic stimulation of the spared allele by artificial transactivators. Small activating RNAs (saRNAs) offer an alternative, appealing approach. As a proof-of-principle, here we tested this approach on the Rett syndrome-linked, haploinsufficient, Foxg1 brain patterning gene. We selected a set of artificial small activating RNAs (saRNAs) upregulating it in neocortical precursors and their derivatives. Expression of these effectors achieved a robust biological outcome. saRNA-driven activation (RNAa) was limited to neural cells which normally express Foxg1 and did not hide endogenous gene tuning. saRNAs recognized target chromatin through a ncRNA stemming from it. Gene upregulation required Ago1 and was associated to RNApolII enrichment throughout the Foxg1 locus. Finally, saRNA delivery to murine neonatal brain replicated Foxg1-RNAa in vivo

Four-noded mixed finite elements, using unsymmetric stresses, for linear analysis of membranes

A family of new 4-noded membrane elements with drilling degrees of freedom and unsymmetric assumed stresses is presented; it is derived from a mixed variational principle originally formulated for finite strain analysis and already used in the literature to develop a purely kinematic membrane model. The performance of these elements, investigated through some well established benchmark problems, is found to be fairly good and their accuracy is comparable with that given by models with a larger number of nodal parameters

Improved non-dimensional dynamic influence function method based on tow-domain method for vibration analysis of membranes

This article introduces an improved non-dimensional dynamic influence function method using a sub-domain method for efficiently extracting the eigenvalues and mode shapes of concave membranes with arbitrary shapes. The non-dimensional dynamic influence function method (non-dimensional dynamic influence function method), which was developed by the authors in 1999, gives highly accurate eigenvalues for membranes, plates, and acoustic cavities, compared with the finite element method. However, it needs the inefficient procedure of calculating the singularity of a system matrix in the frequency range of interest for extracting eigenvalues and mode shapes. To overcome the inefficient procedure, this article proposes a practical approach to make the system matrix equation of the concave membrane of interest into a form of algebraic eigenvalue problem. It is shown by several case studies that the proposed method has a good convergence characteristics and yields very accurate eigenvalues, compared with an exact method and finite element method (ANSYS)

Rotations in computational solid mechanics

A survey of variational principles, which form the basis for computational methods in both continuum mechanics and multi-rigid body dynamics is presented: all of them have the distinguishing feature of making an explicit use of the finite rotation tensor. A coherent unified treatment is therefore given, ranging from finite elasticity to incremental updated Lagrangean formulations that are suitable for accomodating mechanical nonlinearities of an almost general type, to time-finite elements for dynamic analyses. Selected numerical examples are provided to show the performances of computational techniques relying on these formulations. Throughout the paper, an attempt is made to keep the mathematical abstraction to a minimum, and to retain conceptual clarity at the expense of brevity. It is hoped that the article is self-contained and easily readable by nonspecialists. While a part of the article rediscusses some previously published work, many parts of it deal with new results, documented here for the first time