Search results for "Equilibrium equation"

Activity coefficients and Donnan coion exclusion in charged membranes with weak-acid fixed charge groups

1998

Abstract We have studied theoretically the effects that the dissociation equilibrium of weak-acid fixed charge groups (e.g. carboxyl groups) exerts on the mean activity coefficients in charged membranes using a Donnan formalism. The model calculations indicate that unless carbon dioxide is excluded from the external aqueous solution, the pH of the membrane solution can be low enough to affect significantly the effective fixed charge concentration and the coion exclusion when the membrane fixed charge concentration is high compared with the external solution salt concentration. Although this problem was already pointed out in previous studies, the possibility that the pH and salt concentrati…

Gradient elasticity and nonstandard boundary conditions

2003

Abstract Gradient elasticity for a second gradient model is addressed within a suitable thermodynamic framework apt to account for nonlocality. The pertinent thermodynamic restrictions upon the gradient constitutive equations are derived, which are shown to include, besides the field (differential) stress–strain laws, a set of nonstandard boundary conditions. Consistently with the latter thermodynamic requirements, a surface layer with membrane stresses is envisioned in the strained body, which together with the above nonstandard boundary conditions make the body constitutively insulated (i.e. no long distance energy flows out of the boundary surface due to nonlocality). The total strain en…

On the use of SPH for Mechanical Engineering structural analyses: an elastic linear case

2011

Analytical solution for composite layered beam subjected to uniformly distributed load

2016

ABSTRACTThe article presents an analytical theory for multilayered composite beams subjected to transverse uniformly distributed loads. The formulation is based on a layerwise model characterized by third-order approximation of the axial displacements and fourth-order approximation of the transverse displacements. The layerwise kinematical model is rewritten in terms of generalized variables. The beam equilibrium equations, expressed in terms of stress resultant, allow writing the boundary value governing problem. The layerwise fields are obtained by postprocessing steps. The main advantage is to ensure the accuracy level associated to the layerwise formulations preserving the computational…

An analytical solution for multilayered beams subjected to ends loads

2014

An alternative model for multilayered beams undergoing axial, shear and bending loads applied at the beam's ends is developed. It is based on a layer-wise kinematics, which inherently fulfills the equilibrium equations at layer level and the interface continuity conditions. This kinematics is suitably expressed by introducing a set of generalized variables representative of the beam midline displacement field, which become the primary variables of the problem governing equations. As a consequence, the proposed beam model exhibits the computational characteristics of an equivalent single layer model and possesses the accuracy of layer-wise beam theories, as well. Closed form solutions for di…