Search results for "Direct stiffness method"
showing 2 items of 2 documents
Nonlocal elasticity and related variational principles
2001
Abstract The Eringen model of nonlocal elasticity is considered and its implications in solid mechanics studied. The model is refined by assuming an attenuation function depending on the `geodetical distance' between material particles, such that in the diffusion processes of the nonlocality effects certain obstacles as holes or cracks existing in the domain can be circumvented. A suitable thermodynamic framework with nonlocality is also envisaged as a firm basis of the model. The nonlocal elasticity boundary-value problem for infinitesimal displacements and quasi-static loads is addressed and the conditions for the solution uniqueness are established. Three variational principles, nonlocal…
Finite element method for a nonlocal Timoshenko beam model
2014
A finite element method is presented for a nonlocal Timoshenko beam model recently proposed by the authors. The model relies on the key idea that nonlocal effects consist of long-range volume forces and moments exchanged by non-adjacent beam segments, which contribute to the equilibrium of a beam segment along with the classical local stress resultants. The long-range volume forces/moments are linearly depending on the product of the volumes of the interacting beam segments, and their relative motion measured in terms of the pure beam deformation modes, through appropriate attenuation functions governing the spatial decay of nonlocal effects. In this paper, the beam model is reformulated wi…