scholarly journals Analytic bending solutions of free rectangular thin plates resting on elastic foundations by a new symplectic superposition method

2013 ◽  
Vol 469 (2153) ◽  
pp. 20120681 ◽  
Author(s):  
Rui Li ◽  
Yang Zhong ◽  
Ming Li
Keyword(s):  
Finite Element Method ◽  
Symplectic Geometry ◽  
Analytic Solutions ◽  
Thin Plates ◽  
Superposition Method ◽  
The Finite Element Method ◽  
Simple Derivation ◽  
Elastic Foundations ◽  
Winkler Model ◽  
Geometry Method

Analytic bending solutions of free rectangular thin plates resting on elastic foundations, based on the Winkler model, are obtained by a new symplectic superposition method. The proposed method offers a rational elegant approach to solve the problem analytically, which was believed to be difficult to attain. By way of a rigorous but simple derivation, the governing differential equations for rectangular thin plates on elastic foundations are transferred into Hamilton canonical equations. The symplectic geometry method is then introduced to obtain analytic solutions of the plates with all edges slidingly supported, followed by the application of superposition, which yields the resultant solutions of the plates with all edges free on elastic foundations. The proposed method is capable of solving plates on elastic foundations with any other combinations of boundary conditions. Comprehensive numerical results validate the solutions by comparison with those obtained by the finite element method.

scholarly journals Non-linearity of the contact layer between elements joined in a multi-bolted connection and the preload of the bolts

2016 ◽  
Vol 165 (2) ◽  
pp. 3-8
Author(s):  
Rafał GRZEJDA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Cylinder Head ◽  
Contact Layer ◽  
Rigid Support ◽  
The Finite Element Method ◽  
Bolted Connection ◽  
Winkler Model ◽  
Engine Cylinder

The paper presents modeling and calculations of multi-bolted connections at the assembly stage on an example of the engine cylinder head-block connection. The physical model of the connection was introduced as a combination of three subsystems: the set of bolts, the joined element and the contact layer between the joined element and the rigid support. The finite element method (FEM) was used for the modeling. Bolts were replaced with hybrid elements. The joined element was modeled with spatial finite elements. The Winkler model of the contact layer has been taken into consideration. The truth of the theorem has been examined, according to which non-linearity of the contact layer has a negligible impact on the final values of the bolt forces in the case of sequential preloading of the multi-bolted connection. The results of the calculations of a selected multi-bolted connection have been compared with the experimental results.

Thermal Analysis of Thin Plates Using the Finite Element Method

2010 ◽  
Author(s):  
G. K. Er ◽  
V. P. Iu ◽  
X. L. Liu ◽  
Jane W. Z. Lu ◽  
Andrew Y. T. Leung ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Thermal Analysis ◽  
Finite Element ◽  
Thin Plates ◽  
The Finite Element Method ◽  
Element Method

scholarly journals Analysis of beams on elastic foundations using Green's functions

2021 ◽  
Vol 37 (2) ◽  
Author(s):  
J. Molina-Villegas ◽  
J. Ortega ◽  
A. Toro
Keyword(s):  
Finite Element Method ◽  
Elastic Foundation ◽  
Low Cost ◽  
Retaining Walls ◽  
Complex Structures ◽  
The Finite Element Method ◽  
Elastic Foundations ◽  
Stiffness Method ◽  
Model Foundation ◽  
Beams On Elastic Foundation

Beams on elastic foundation are basic elements within structural analysis, which are used to model foundation beams, foundation piles, retaining walls, and more complex structures that include some of these elements. For their analysis, the finite element method is usually used [1], which produces an approximate solution of the problem; and the Green's function stiffness method [2], which produces an exact solution. This article presents a methodology 100% based on the use of Green function's (response to a unit point force), to obtain the exact response of beams on elastic foundation. The main advantage of this formulation is its computational low cost compared to the aforementioned alternatives, and even for a large number of problems, it can be expressed only by means of sums and integrals, which can be easily performed numerically. Also, a great variety of Green function's for finite and infinite beams on elastic foundations with different boundary conditions are also presented, as well as some examples with the implementation of the proposed methodology.

scholarly journals Dynamic analysis of complex spacial frame systems by the finite element method

1986 ◽  
Vol 8 (2) ◽  
pp. 21-26
Author(s):  
Nguyen Ngoc Ve
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Static Load ◽  
Equations Of Motion ◽  
Element Model ◽  
Superposition Method ◽  
Direct Integration ◽  
The Finite Element Method ◽  
Mode Superposition Method ◽  
Frame Systems

Numerical simula1ion of complex special frame systems subjected to static load dynamic load and base acceleration is formulated. A finite element model is applied therein the, complex nodes and the foundation influence are considered. Equations of motion are soviet afterontively by step-by-step direct integration and mode superposition method. A number of illustrated  example are computed by the numerical superpose FRADYN), which can be used directly in the field of staeciural design.

Analytical free vibration solutions of fully free orthotropic rectangular thin plates on two-parameter elastic foundations by the symplectic superposition method

2020 ◽  
pp. 107754632096782
Author(s):  
Xin Su ◽  
Eburilitu Bai
Keyword(s):  
Free Vibration ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Superposition Method ◽  
Elastic Foundations ◽  
Vibration Problem ◽  
Separation Variable ◽  
Vibration Problems ◽  
Two Parameter ◽  
Free Edges

The free vibration of orthotropic rectangular thin plates with four free edges on two-parameter elastic foundations is studied by the symplectic superposition method. Firstly, by analyzing the boundary conditions, the original vibration problem is converted into two sub-vibration problems of the plates slidingly clamped at two opposite edges. Based on slidingly clamped at two opposite edges, the fundamental solutions of these two sub-vibration problems are respectively derived by the separation variable method of the corresponding Hamiltonian system, and then the symplectic superposition solution of the original vibration problem is obtained by superimposing the fundamental solutions of the two sub-problems. Finally, the symplectic superposition solution obtained in this study is verified by calculating the frequencies and mode functions of several concrete rectangular thin plates with four free edges.

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