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Integration Error (integration + error)
Selected AbstractsFinite element formulation and algorithms for unsaturated soils.INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2003Part I: Theory Abstract This paper presents a complete finite-element treatment for unsaturated soil problems. A new formulation of general constitutive equations for unsaturated soils is first presented. In the incremental stress,strain equations, the suction or the pore water pressure is treated as a strain variable instead of a stress variable. The global governing equations are derived in terms of displacement and pore water pressure. The discretized governing equations are then solved using an adaptive time-stepping scheme which automatically adjusts the time-step size so that the integration error in the displacements and pore pressures lies close to a specified tolerance. The non-linearity caused by suction-dependent plastic yielding, suction-dependent degree of saturation, and saturation-dependent permeability is treated in a similar way to the elastoplasticity. An explicit stress integration scheme is used to solve the constitutive stress,strain equations at the Gauss point level. The elastoplastic stiffness matrix in the Euler solution is evaluated using the suction as well as the stresses and hardening parameters at the start of the subincrement, while the elastoplastic matrix in the modified Euler solution is evaluated using the suction at the end of the subincrement. In addition, when applying subincrementation, the same rate is applied to all strain components including the suction. Copyright © 2003 John Wiley & Sons, Ltd. [source] Correlation method for variance reduction of Monte Carlo integration in RS-HDMRJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 3 2003Genyuan Li Abstract The High Dimensional Model Representation (HDMR) technique is a procedure for efficiently representing high-dimensional functions. A practical form of the technique, RS-HDMR, is based on randomly sampling the overall function and utilizing orthonormal polynomial expansions. The determination of expansion coefficients employs Monte Carlo integration, which controls the accuracy of RS-HDMR expansions. In this article, a correlation method is used to reduce the Monte Carlo integration error. The determination of the expansion coefficients becomes an iteration procedure, and the resultant RS-HDMR expansion has much better accuracy than that achieved by direct Monte Carlo integration. For an illustration in four dimensions a few hundred random samples are sufficient to construct an RS-HDMR expansion by the correlation method with an accuracy comparable to that obtained by direct Monte Carlo integration with thousands of samples. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 277,283, 2003 [source] A study on the convergence of least-squares meshfree method under inaccurate integrationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003Sang-Hoon Park Abstract In the authors' previous work, it has been shown through numerical examples that the least-squares meshfree method (LSMFM) is highly robust to the integration errors while the Galerkin meshfree method is very sensitive to them. A mathematical study on the convergence of the solution of LSMFM under inaccurate integration is presented. New measures are introduced to take into account the integration errors in the error estimates. It is shown that, in LSMFM, solution errors are bounded by approximation errors even when integration is not accurate. Copyright © 2003 John Wiley & Sons, Ltd. [source] An optimization procedure for the pultrusion process based on a finite element formulationPOLYMER COMPOSITES, Issue 3 2002R. M. L. Coelho Composite materials are manufactured by different processes. In all, the process variables have to be analyzed in order to obtain a part with uniform mechanical properties. In the pultrusion process, two variables are the most important: the pulling speed of resin-impregnated fibers and the temperature profile (boundary condition) imposed on the mold wall. Mathematical modeling of this process results in partial differential equations that are solved here by a detailed procedure based on the Galerkin weighted residual finite element method. The combination of the Picard and Newton-Raphson methods with an analytical Jacobian calculation proves to be robust, and a mesh adaptation procedure is presented in order to avoid integration errors during the process optimization. The two earlier-mentioned variables are optimized by the Simulated Annealing method with some constraints, such as a minimum degree of cure at the end of the process, and the resin degradation (the part temperature cannot be higher than the resin degradation temperature at any time during the whole process). Herein, the proposed objective function is an economic criterion instead of the pulling speed of resin-impregnated fibers, used in the majority of papers. [source] | ||||||||||