Search results for "Boundary value problem"
showing 10 items of 551 documents
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, …
An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems
2015
The recently developed approximate Wiener path integral (WPI) technique for determining the stochastic response of nonlinear/hysteretic multi-degree-of-freedom (MDOF) systems has proven to be reliable and significantly more efficient than a Monte Carlo simulation (MCS) treatment of the problem for low-dimensional systems. Nevertheless, the standard implementation of the WPI technique can be computationally cumbersome for relatively high-dimensional MDOF systems. In this paper, a novel WPI technique formulation/implementation is developed by combining the “localization” capabilities of the WPI solution framework with an appropriately chosen expansion for approximating the system response PDF…
Strain-gradient elastic-plastic material models and assessment of the higher order boundary conditions
2007
Abstract A gradient elastic material model exhibiting gradient kinematic and isotropic hardening is addressed within a thermodynamic framework suitable to cope with nonlocal-type continua. The Clausius–Duhem inequality is used, in conjunction with the concepts of energy residual, insulation condition and locality recovery condition, to derive all the pertinent restrictions upon the constitutive equations, including the PDEs and the related higher order (HO) boundary conditions that govern the gradient material behaviour. Through a suitable limiting procedure, the HO boundary conditions are shown to interpret the action, upon the body's boundary surface, of idealized extra HO constraints cap…
A four-node MITC finite element for magneto-electro-elastic multilayered plates
2013
An isoparametric four-node finite element for multilayered magneto-electro-elastic plates analysis is presented. It is based on an equivalent single-layer model, which assumes the first order shear deformation theory and quasi-static behavior for the electric and magnetic fields. First, the electro-magnetic state of the plate is determined in terms of the mechanical primary variables, namely the generalized displacements, by solving the strong form of the magneto-electric governing equations coupled with the electro-magnetic interface continuity conditions and the external boundary conditions. In turn, this result is used into the layers constitutive law to infer the equivalent single-layer…
A finite element formulation for large deflection of multilayered magneto-electro-elastic plates
2014
An original finite element formulation for the analysis of large deflections in magneto-electro-elastic multilayered plates is presented. The formulation is based on an equivalent single-layer model in which first order shear deformation theory with von Karman strains and quasi-static behavior for the electric and magnetic fields are assumed. To obtain the plate model, the electro-magnetic state is firstly determined and condensed to the mechanical primary variables, namely the generalized displacements. In turn, this result is used to obtain laminate effective stiffness coefficients that allow to express the plate mechanical stress resultants in terms of the generalized displacements and a…
ON THE UNIT CELL BOUNDARY VALUE PROBLEM WITH MESHLESS FORMULATION FOR MASONRY STRUCTURES
2017
In a generic multi-scale computational homogenization (CH) procedure, the crucial point is the definition and the solution of the Unit Cell (UC) Boundary Value Problem (BVP). The main aspects to be chosen for the formulation of the UC BVP are: (i) geometry; (ii) bound- ary conditions (BCs); (iii) material models; (iv) numerical approximation techniques. All these components play a key-role in the efficiency of the multi-scale procedure. In the present study, the UC BVP is formulated for running bond masonry according to a dis- placement based variational formulation, where the material of the blocks is considered indefi- nitely elastic and the mortar joints are simulated by zero-thickness e…
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.
Variational Formulations for Coupled BE/FE Methods in Elastostatics
1994
Ein gekoppeltes BEM/FEM-Problem aus der Elastostatik, ein typisches Substrukturproblem, wird im Rahmen der symmetrisch-definiten BEM behandelt. Es werden vier verschiedene Variationsformulierungen vorgestellt, in deren jeder die Transmissionsbedingungen gegenuber der Trennflache zwischen FE-Unterregion und BE-Unterregion die Rolle naturlicher Randbedingungen spielen. Zwei der oben erwahnten Formulierungen sind Stationaritatsprinzipien in gemischter Form, die anderen beiden sind Sattelpunkt-Prinzipien, d. h. Kombinationen des Rand-min-max-Prinzips entweder mit dem Prinzip der minimalen Gesamtpotentialenergie oder mit dem Prinzip der minimalen Gesamtkomplementaritatsenergie. Jedes der oben an…
Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian
2004
AbstractThis paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [Topol. Methods Nonlinear Anal. 22 (2003) 93–104].
On a mixed boundary value problem involving the p-Laplacian
2011
In this paper we prove the existence of infinitely many solutions for a mixed boundary value problem involving the one dimensional p-Laplacian. A result on the existence of three solutions is also established. The approach is based on multiple critical points theorems.