Search results for "Stiffness matrix"
showing 10 items of 20 documents
Acoustic modes in metallic nanoparticles: atomistic versus elasticity modeling
2009
The validity of the linear elasticity theory is examined at the nanometer scale by investigating the vibrational properties of silver and gold nanoparticles whose diameters range from about 1.5 to 4 nm. Comparing the vibration modes calculated by elasticity theory and atomistic simulation based on the Embedded Atom Method, we first show that the anisotropy of the stiffness tensor in elastic calculation is essential to ensure a good agreement between elastic and atomistic models. Second, we illustrate the reduction of the number of vibration modes due to the diminution of the number of atoms when reducing the nanoparticles size. Finally, we exhibit a breakdown of the frequency-spectra scalin…
A thermodynamic approach to nonlocal plasticity and related variational principles
1999
Elastic-plastic rate-independent materials with isotropic hardening/softening of nonlocal nature are considered in the context of small displacements and strains. A suitable thermodynamic framework is envisaged as a basis of a nonlocal associative plasticity theory in which the plastic yielding laws comply with a (nonlocal) maximum intrinsic dissipation theorem. Additionally, the rate response problem for a (continuous) set of (macroscopic) material particles, subjected to a given total strain rate field, is discussed and shown to be characterized by a minimum principle in terms of plastic coefficient. This coefficient and the relevant continuum tangent stiffness matrix are shown to admit, …
Direct stiffness matrices of BEs in the Galerkin BEM formulation
2001
Abstract In the analysis of an elastic two-dimensional solid body by means of the Symmetric Galerkin Boundary Element Method (SGBEM), difficulties arise in the computation of some terms of the solving system coefficients. In fact these coefficients are expressed as double integrals with singularities of order 1/ r 2 , r being the distance between the field and source points. In order to compute these coefficients a strategy based on Schwartz's distribution theory is employed. In this paper the direct stiffness matrix related to the generic node of the free boundary are computed in closed form.
A FE-Meshless Multiscale Approach for Masonry Materials
2015
Abstract A FE-Meshless multiscale computational strategy for the analysis of running bond masonry is presented. The Meshless Method (MM) is adopted to solve the boundary value problem (BVP) at the mesoscopic level. The representative unit cell is composed by the aggregate and the surrounding joints, the former assumed to behave elastically while the latter are simulated as non-associated elastic-plastic zero-thickness interfaces with a softening response. Macroscopic localization of plastic bands is obtained performing a spectral analysis of the tangent stiffness matrix. Localized plastic bands are embedded into the quadrature points area of the macroscopic finite elements.
CH of masonry materials via meshless meso-modeling
2014
In the present study a multi-scale computational strategy for the analysis of masonry structures is presented. The structural macroscopic behaviour is obtained making use of the Computational Homogenization (CH) technique based on the solution of the boundary value problem (BVP) of a detailed Unit Cell (UC) chosen at the meso-scale and representative of the heterogeneous material. The smallest UC is composed by a brick and half of its surrounding joints, the former assumed to behave elastically while the latter considered with an elastoplastic softening response. The governing equations at the macroscopic level are formulated in the framework of finite element method while the Meshless Meth…
The multiple slope discontinuity beam element for nonlinear analysis of RC framed structures
2018
The seismic nonlinear response of reinforced concrete structures permits to identify critical zones of an existing structure and to better plan its rehabilitation process. It is obtained by performing finite element analysis using numerical models classifiable into two categories: lumped plasticity models and distributed plasticity models. The present work is devoted to the implementation, in a finite element environment, of an elastoplastic Euler–Bernoulli beam element showing possible slope discontinuities at any position along the beam span, in the framework of a modified lumped plasticity. The differential equation of an Euler–Bernoulli beam element under static loads in presence of mul…
Stability analysis of an electromagnetically levitated sphere
2006
We present a combined numerical and analytical approach to analyze the static and dynamic stabilities of an electromagnetically levitated spherical body depending on the ac frequency and the configuration of a three-dimensional (3D) coil made of thin winding which is modeled by linear current filaments. First, we calculate numerically the magnetic vector potential in grid points on the surface of the sphere and then use Legendre and fast Fourier transforms to find the expansion of the magnetic field in terms of spherical harmonics. Second, we employ a previously developed gauge transformation to solve analytically the 3D electromagnetic problem in terms of the numerically obtained expansion…
Magnus and Fer expansions for matrix differential equations: the convergence problem
1998
Approximate solutions of matrix linear differential equations by matrix exponentials are considered. In particular, the convergence issue of Magnus and Fer expansions is treated. Upper bounds for the convergence radius in terms of the norm of the defining matrix of the system are obtained. The very few previously published bounds are improved. Bounds to the error of approximate solutions are also reported. All results are based just on algebraic manipulations of the recursive relation of the expansion generators.
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…
Estimation of the elastic constants of highly porous cellular plastics reinforced with fibres embedded in foam struts
2015
In order to enhance the mechanical properties of polymer foams, fillers of different materials and sizes are being applied. Fibrous fillers shorter than the characteristic foam cell dimensions have the potential of efficient reinforcement, due to their high aspect ratio, without detrimentally interfering with foam structure. A theoretical model is developed for evaluation of the effect of filler on foam stiffness. The elastic response of rigid polymer foams filled with short fibres, of length commensurable with that of foam struts, is modelled by using the orientational averaging technique. Explicit expressions for components of the stiffness tensor of composite foams are derived in terms …