Galerkin method

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

In this study two types of MEE plates, namely BaTiO3 and CoFe2O4 were considered. The basic equations are derived using classical plate theory with nonlocal stress theory and are solved using the Galerkin method and Runge-Kutta method.

13p viambani 18-06-2024 1 1   Download

This paper investigates the nonlinear vibration of saturated porous functionally graded plate subjected to the combination of mechanical and thermal loadings. Three different distributions of porosity are considered. Based on the Biot and higher order shear deformation theories, the vibration characteristics including natural frequency, deflection amplitude – time curves and relation between frequency ratio and amplitude of the saturated porous plate are determined.

13p viambani 18-06-2024 1 1   Download

A theoretical study of sound transmission loss across a simply supported double-composite sandwich plate filled with poroplastic material is formulated. Biot's theory is employed to describe wave propagation in elastic porous media. The two face composite plates are modeled as classical thin plates. By using the modal superposition theory, a double series solution for the sound transmission loss of the structure is obtained with the help of the Galerkin method.

10p dathienlang1012 03-05-2024 0 0   Download

Viscous dampers are used widely to mitigate cable vibrations cable-stayed bridges. A damper attached to a stay cable leads to complex modes. The complexity can highly affect the aeroelastic stability of the cable. A galloping instability analysis of cable with an attached damper will be presented.

8p vimarillynhewson 02-01-2024 3 3   Download

The circular plates and shallow spherical caps are assumed to be subjected to uniformly distributed thermal loads. By applying the Galerkin method, the relations between thermal load-deflection are achieved to determine the postbuckling behavior and critical buckling loads of the considered structures.

13p viwolverine 11-07-2023 3 2   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

Phương pháp phần tử hữu hạn (Finite Element Method – FEM) được xem là 1 phương pháp số mạnh và hữu dụng trong việc giải quyết thành công nhiều bài toán cơ học. Bài viết trình bày việc sử dụng phương pháp EFG với phép xấp xỉ bình phương tối thiểu động (MLS) để nghiên cứu dao động tự do cho thanh và dầm.

5p vicaptainmarvel 21-04-2023 7 2   Download

In the paper "Global attractors for semilinear parabolic equations with delays", we prove the existence and upper semicontinuity of global attractors with respect to parameters for semilinear parabolic equations with general delays. The obtained results recover and extend some known ones about a non-local PDE with the stateselective delay in [10].

18p runordie5 04-07-2022 1 1   Download

This work deals with the nonlinear buckling and post-buckling of stiffened nanocomposite plates reinforced functionally graded carbon nanotubes (FG CNTRC) resting on elastic foundation in thermal environment. Obtained results showed that the properties of the nanocomposited plates embedded with single-walled carbon nanotubes are dependent on temperature and altered according to linear functions of the thickness.

24p vimelindagates 18-07-2022 11 3   Download

In the mechanisms and machines operating at high speeds, the elastic vibration of links is inevitable. In this paper the dynamic modeling and controller design for a flexible four-bar mechanism are studied. The fully coupled non-linear equations of motion are obtained by using the Lagrange’s equations with multipliers for constrained multibody systems. The resulting differential-algebraic equations are solved using numerical methods. A simple PD controller is designed to reduce the influence of the elastic link on the desired motion.

5p cothumenhmong11 10-05-2021 21 2   Download

The nonlinear free vibration of embedded nanotubes under longitudinal magnetic field is studied in this paper. The governing equation for the nanotube is formulated by employing Euler–Bernoulli beam model and the nonlocal strain gradient theory. The analytical expression of the nonlinear frequency of the nanotube is obtained by using Galerkin method and the equivalent linearization method with the weighted averaging value. The accuracy of the obtained solution has been verified by comparison with the published solutions and the exact solution.

23p nguaconbaynhay11 07-04-2021 19 2   Download

This paper is concerned with the nonlinear dynamic buckling of sandwich functionally graded circular cylinder shells filled with fluid. Governing equations are derived using the classical shell theory and the geometrical nonlinearity in von Karman–Donnell sense is taken into account. Solutions of the problem are established by using Galerkin’s method and Runge–Kutta method. Effects of thermal environment, geometric parameters, volume fraction index k and fluid on dynamic critical loads of shells are investigated.

14p nguaconbaynhay11 07-04-2021 14 1   Download

The dynamic response to variable magnitude moving distributed masses of simply supported non-uniform Bernoulli–Euler beam resting on Pasternak elastic foundation is investigated in this paper. The problem is governed by fourth order partial differential equation with variable and singular coefficients. The main objective of this work is to obtain closed form solution to this class of dynamical problem.

16p nguaconbaynhay11 07-04-2021 7 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

This study analyses the hydrodynamic characteristic of the tilting pad thrust bearing. Research content is simultaneously solving the Reynolds equation, force equilibrium equation, and momentum equilibrium equations. Reynolds equation is solved by utilizing the finite element method with Galerkin weighted residual, thereby determines the pressure at each discrete node of the film. Force and momentums are integrated from pressure nodes by Gaussian integral.

6p trinhthamhodang1218 04-03-2021 18 1   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

A cantilever beam is a well-known structural element in engineering, which is only fixed at one end. This structure can be used to describe a manipulator, whose stiffness is large to ensure rigidity and stability of the system. A flexible cantilever beam provides a light-weight structure and high cost efficiency but generates vibration under high-speed positioning. In this paper, we aim to control the vibratory behavior of a flexible cantilever beam attached to a moving hub.

9p trinhthamhodang9 04-12-2020 11 1   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

The study results for dynamic response of PFGCP present the effect of geometrical ratio, elastic foundations: Winkler foundation and Paskternak foundation; loads: mechanical load and thermal load; and the material properties and distribution type of porosity. The results are shown numerically and are determined by using Galerkin methods and Fourth-order Runge-Kutta method.

21p tamynhan6 14-09-2020 20 3   Download