Galerkin approximations

Part 1 of ebook "The finite element method for solid and structural mechanics (Seventh edition)" provides readers with contents including: Chapter 1 - General problems in solid mechanics and nonlinearity; Chapter 2 - Galerkin method of approximation, irreducible and mixed forms; Chapter 3 - Solution of nonlinear algebraic equations; Chapter 4 - Inelastic and nonlinear materials; Chapter 5 - Geometrically nonlinear problems, finite deformation; Chapter 6 - Material constitution for finite deformation; Chapter 7 - Material constitution using representative volume elements;...

310p giangmacvien 21-06-2024 0 0   Download

The present investigation analyses the critical buckling studies of triple-walled carbon nanotube using the Euler–Bernoulli model. The present study deals with three different boundary conditions, namely, simply-simply, clamped-clamped, and clampedsimply supported carbon nanotube.

21p viwolverine 11-07-2023 4 2   Download

In this paper, we investigate the existence, uniqueness, and continuity of weak solutions with respect to initial values for a nonlinear parabolic equation of reactiondiffusion nonlocal type by an application of the Faedo-Galerkin approximation and AubinLions- Simon compactness results.

11p trinhthamhodang1218 18-03-2021 6 1   Download

In this paper, we study the first initial boundary value problem for a class of quasilinear degenerate parabolic equations involving weighted p-Laplacian operators. The existence and uniqueness of a weak solution with respect to initial values is ensured by an application of the Faedo - Galerkin approximation and compact method. Moreover, the longtime behavior of solutions to that problem is considered via the concept of global attractors in various bi-spaces.

15p trinhthamhodang1218 18-03-2021 13 3   Download

In this paper, on the base of the discrepancy principle for regularization parameter choice, the convergence rates of the regularized solution as well as its Galerkin approximations for nonlinear ill-posed problems with m-accretive perturbations are established without demanding the weak continuity of the duality mapping of the Banach spaces.

8p tamynhan5 10-12-2020 8 2   Download

The paper presents a new approach to the conventional averaging in which the role of boundary values is considered in a more detailed way. It results in a new weighted local averaging operator (WLAO) taking into account the particular role of boundary values. A remarkable feature of WLAO is that this operator contains a parameter of boundary regulation p and depends on a local value h of the integration domain. By varying these two parameters one can regulate the obtained approximate solutions in order to get more accurate ones.

14p trinhthamhodang9 10-12-2020 8 0   Download

In this paper we prove the well-posedness of weak solutions to a semilinear heat equation with memory and the nonlinearity f of exponential type by the Galerkin approximation and compactness method. The main novelty of our result is that no restriction on the growth of the nonlinearities is imposed.

10p vigeorgia2711 01-12-2020 20 2   Download

. In this paper an approximate analytical solution to analyze the nonlinear buckling and postbuckling behavior of imperfect functionally graded panels with the Poisson’s ratio also varying smoothly along the thickness is investigated. Based on the classical shell theory and von Karman’s assumption of kinematic nonlinearity and applying Galerkin procedure, the equations for finding critical loads and load-deflection curves of cylindrical panel subjected to axial compressive load with two types boundary conditions, are given.

18p thienthanquydu 17-10-2018 27 0   Download