Search results for "Modeling and simulation"
showing 10 items of 1561 documents
Mechanically-based approach to non-local elasticity: Variational principles
2010
Abstract The mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products. Such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle. The constitutive relations between dual variables are introduced defining a proper, convex, potential energy. It is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional. Mo…
One-dimensional heterogeneous solids with uncertain elastic modulus in presence of long-range interactions: Interval versus stochastic analysis
2013
The analysis of one-dimensional non-local elastic solids with uncertain Young's modulus is addressed. Non-local effects are represented as long-range central body forces between non-adjacent volume elements. For comparison purpose, the fluctuating elastic modulus of the material is modeled following both a probabilistic and a non-probabilistic approach. To this aim, a novel definition of the interval field concept, able to limit the overestimation affecting ordinary interval analysis, is introduced. Approximate closed-form expressions are derived for the bounds of the interval displacement field as well as for the mean-value and variance of the stochastic response.
Fundamental solutions for general anisotropic multi-field materials based on spherical harmonics expansions
2016
Abstract A unified method to evaluate the fundamental solutions for generally anisotropic multi-field materials is presented. Based on the relation between the Rayleigh expansion and the three-dimensional Fourier representation of a homogenous partial differential operator, the proposed technique allows to obtain the fundamental solutions and their derivatives up to the desired order as convergent series of spherical harmonics. For a given material, the coefficients of the series are computed only once, and the derivatives of the fundamental solutions are obtained without any term-by-term differentiation, making the proposed approach attractive for boundary integral formulations and efficie…
Coupled VEM–BEM Approach for Isotropic Damage Modelling in Composite Materials
2023
Numerical prediction of composite damage behaviour at the microscopic level is still a challenging engineering issue for the analysis and design of modern materials. In this work, we document the application of a recently developed numerical technique based on the coupling between the virtual element method (VEM) and the boundary element method (BEM) within the framework of continuum damage mechanics (CDM) to model the in-plane damage evolution characteristics of composite materials. BEM is a widely adopted and efficient numerical technique that reduces the problem dimensionality due to its underlying formulation. It substantially simplifies the pre-processing stage and decreases the compu…
Coupling BEM and VEM for the Analysis of Composite Materials with Damage
2021
Numerical tools which are able to predict and explain the initiation and propagation of damage at the microscopic level in heterogeneous materials are of high interest for the analysis and design of modern materials. In this contribution, we report the application of a recently developed numerical scheme based on the coupling between the Virtual Element Method (VEM) and the Boundary Element Method (BEM) within the framework of continuum damage mechanics (CDM) to analyze the progressive loss of material integrity in heterogeneous materials with complex microstructures. VEM is a novel numerical technique that, allowing the use of general polygonal mesh elements, assures conspicuous simplific…
Stress gradient versus strain gradient constitutive models within elasticity
2014
Abstract A stress gradient elasticity theory is developed which is based on the Eringen method to address nonlocal elasticity by means of differential equations. By suitable thermodynamics arguments (involving the free enthalpy instead of the free internal energy), the restrictions on the related constitutive equations are determined, which include the well-known Eringen stress gradient constitutive equations, as well as the associated (so far uncertain) boundary conditions. The proposed theory exhibits complementary characters with respect to the analogous strain gradient elasticity theory. The associated boundary-value problem is shown to admit a unique solution characterized by a Helling…
Special Splines of Exponential Type for the Solutions of Mass Transfer Problems in Multilayer Domains
2016
We consider averaging methods for solving the 3-D boundary-value problem of second order in multilayer domain. The special hyperbolic and exponential type splines, with middle integral values of piece-wise smooth function interpolation are considered. With the help of these splines the problems of mathematical physics in 3-D with piece-wise coefficients are reduced with respect to one coordinate to 2-D problems. This procedure also allows to reduce the 2-D problems to 1-D problems and the solution of the approximated problemsa can be obtained analytically. In the case of constant piece-wise coefficients we obtain the exact discrete approximation of a steady-state 1-D boundary-value problem.…
Asynchronous Runtime Verification of Business Processes: Proof of Concept
2020
Two -methods to generate Bézier surfaces from the boundary
2009
Two methods to generate tensor-product Bezier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of @D^4x->=0 with prescribed boundary and adjacent to the boundary control points of a nxn Bezier surface. The second one is based on the nonhomogeneous biharmonic equation @D^2x->=p, where p could be understood as a vectorial load adapted to the C^1-boundary conditions.
Bézier surfaces of minimal area: The Dirichlet approach
2004
The Plateau-Bezier problem consists in finding the Bezier surface with minimal area from among all Bezier surfaces with prescribed border. An approximation to the solution of the Plateau-Bezier problem is obtained by replacing the area functional with the Dirichlet functional. Some comparisons between Dirichlet extremals and Bezier surfaces obtained by the use of masks related with minimal surfaces are studied.