Search results for "Mathematical analysis"
showing 10 items of 2409 documents
A Boundary/Interior Element Discretization Method for the Analysis of Two- and Three-Dimensional Elastic-Plastic Structures
1992
A coupled boundary/interior element method is presented for the analysis of elastic-plastic structures with material models endowed of dual internal variables. The domain field modelling is limited to the only plastic strains and strain-like internal variables, represented by their node values at a set of strain points in each interior element. The formulation, based on a Galerkin-type approach, is variationally consistent and leads to a fully symmetric-definite equation system. The backward difference method is adopted for the step-by-step integration procedure, and each step is addressed by an iterative predictor/corrector solution scheme. The analysis method is expected to be most approp…
Approximation of Elliptic Hemivariational Inequalities
1999
From the previous chapter we know that there exist many important problems in mechanics in which constitutive laws are expressed by means of nonmonotone, possibly multivalued relations (nonmonotone multivalued stress-strain or reaction-displacement relations,e.g). The resulting mathematical model leads to an inclusion type problem involving multivalued nonmonotone mappings or to a substationary type problem for a nonsmooth, nonconvex superpotential expressed in terms of calculus of variation. It is the aim of this chapter to give a detailed study of a discretization of such a type of problems including the convergence analysis. Here we follow closely Miettinen and Haslinger, 1995, Miettinen…
High Order Compact Finite Difference Schemes for A Nonlinear Black-Scholes Equation
2001
A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.
Method of Lines and Finite Difference Schemes with Exact Spectrum for Solving Some Linear Problems of Mathematical Physics
2013
In this paper linear initial-boundary-value problems of mathematical physics with different type boundary conditions BCs and periodic boundary conditions PBCs are studied. The finite difference scheme FDS and the finite difference scheme with exact spectrum FDSES are used for the space discretization. The solution in the time is obtained analytically and numerically, using the method of lines and continuous and discrete Fourier methods.
Perimeter symmetrization of some dynamic and stationary equations involving the Monge-Ampère operator
2017
We apply the perimeter symmetrization to a two-dimensional pseudo-parabolic dynamic problem associated to the Monge-Ampere operator as well as to the second order elliptic problem which arises after an implicit time discretization of the dynamical equation. Curiously, the dynamical problem corresponds to a third order operator but becomes a singular second order parabolic equation (involving the 3-Laplacian operator) in the class of radially symmetric convex functions. Using symmetrization techniques some quantitative comparison estimates and several qualitative properties of solutions are given.
Symmetric Galerkin Boundary Element Methods
1998
This review article concerns a methodology for solving numerically, for engineering purposes, boundary and initial-boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form. The discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager’s sense. As main con…
The indirect force method
1990
Abstract It is known that the matrix force method shows some advantages over the displacement method for certain classes of problems, particularly in optimization and in the stress concentration analysis. Notwithstanding this, few efforts have been made to employ this method in engineering problems. In this paper, within the elastic analysis of frames and trusses, the indirect force method, utilizing beam-node type finite elements, is proposed. This method is based on the kinematical and mechanical study of nodes and of beams, the latter connected with the nodes by their first extremes according to a preliminary arrangement. In this formulation kinematical singularities are included, in the…
High-fidelity analysis of multilayered shells with cut-outs via the discontinuous Galerkin method
2021
Abstract A novel numerical method for the analysis of multilayered shells with cut-outs is presented. In the proposed approach, the shell geometry is represented via either analytical functions or NURBS parametrizations , while generally-shaped cut-outs are defined implicitly within the shell modelling domain via a level set function . The multilayered shell problem is addressed via the Equivalent-Single-Layer approach whereby high-order polynomial functions are employed to approximate the covariant components of the displacement field throughout the shell thickness. The shell governing equations are then derived from the Principle of Virtual Displacements of three-dimensional elasticity an…
A coupled Finite Volume–Smoothed Particle Hydrodynamics method for incompressible flows
2016
Abstract An hybrid approach is proposed which allows to combine Finite Volume Method (FVM) and Smoothed Particle Hydrodynamics (SPH). The method is based on the partitioning of the computational domain into a portion discretized with a structured grid of hexahedral elements (the FVM-domain ) and a portion filled with Lagrangian particles (the SPH-domain ), separated by an interface made of triangular elements. A smooth transition between the solutions in the FVM and SPH regions is guaranteed by the introduction of a layer of grid cells in the SPH-domain and of a band of virtual particles in the FVM one (both neighboring the interface), on which the hydrodynamic variables are obtained throug…
Symmetric BEM Formulations for Elastic-Damage Material Models
1997
BEM analysis for elastic-damage materials is addressed by “undamaged” fundamental solutions. In step-by-step analysis, the actual response is obtained by an iterative procedure in which the undamaged structure is subjected to the loads and to some fictitious strains (or relaxation stresses) simulating the damage effects. Through symmetric BEM, the solution to the typical iteration problem is shown to solve a boundary/domain stationarity principle, whereas the above iterative procedure can be incorporated in a predictor/corrector scheme aimed at the integration of the damage laws. Discretization by boundary and interior elements leads to a symmetric equation system.