We present a set of explicit conditions, involving the components of the elastic stiffness tensor, which are necessary and sufficient to ensure the strong ellipticity of an orthorhombic incompressible medium. The derivation is based on the procedure developed by Zee and Sternberg (Arch. Rat. Mech. Anal. 83 (1983)) and, consequently, is also applicable to the case of the homogeneously pre-stress...

   The main purpose of the present investigation is to analyze more comprehensively the size-dependent nonlinear free vibration response of multilayer functionally graded graphene platelet-reinforced composite (GPLRC) nanobeams. As a consequence, both of the hardening stiffness and softening stiffness of size effect are taken into consideration by implementation of the nonlocal str...

In a traditional finite element method for the simulation of deformable objects, the stiffness matrix depends on the shape of the tetrahedral elements. Ill-shaped elements containing large or small dihedral angles lead to an arbitrary large condition number of the stiffness matrix, thus slowing down the simulation. In addition, high modal frequencies cannot be simulated stably if an explicit nu...

We have performed coarse-grained molecular-dynamics simulations on both flexible and semiflexible multi-bead-spring model polymer brushes in the presence of explicit solvent particles, to explore their tribological and structural behaviors. The effect of stiffness and tethering density on equilibrium-brush height is seen to be well reproduced within a Flory-type theory. After discussing the equ...

A fully implicit iterative integration procedure is developed for local and geographically distributed hybrid simulation of the seismic response of complex structural systems with distributed nonlinear behavior. The purpose of this procedure is to allow experimental elements in simulations using existing fully implicit integration algorithms designed for pure numerical simulations. The implemen...

although explicit and implicit knowledge of language learners are essential to theoretical and pedagogical debates in second language acquisition (sla), little research has addressed the effects of instructional interventions on the two knowledge types (r. ellis, 2005).this study examined the relative effectiveness of explicit and implicit types of form-focused instruction (ffi) on the acquisit...

Explicit numerical methods for the solution of a system of stiff differential equations suffer from a time step size that approaches zero in order to satisfy stability conditions. Implicit schemes allow a larger time-step, but require more computations. When the differential equations are dominated by a skew-symmetric component, the problem is not stiffness in the sense that the size of the eig...

Additive Runge Kutta (ARK) methods are investigated for application to the spatially discretized one dimensional convection diffusion reaction (CDR) equations. First, accuracy, stability, conservation, and dense output are considered for the general case when N different Runge Kutta methods are grouped into a single composite method. Then, implicit explicit, N = 2, additive Runge Kutta (ARK2) m...

In the numerical simulation of transient reacting flow, standard explicit calculation is prohibitively expensive because of the small time steps needed to address the stiffness of a governing differential system. To circumvent this, new hybrid implicit–explicit methods proposed treat the stiffness, whereas the underlying time-step control is governed by the Courant stability criterion. Because ...