An iterative calculation method for hanger tensions and the cable shape of a suspension bridge based on the catenary theory and finite element method

2018 ◽  
Vol 22 (7) ◽  
pp. 1566-1578 ◽  
Author(s):  
Wen-ming Zhang ◽  
Tao Li ◽  
Lu-yao Shi ◽  
Zhao Liu ◽  
Kai-rui Qian
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Iterative Method ◽  
Numerical Test ◽  
Iteration Process ◽  
Suspension Bridge ◽  
Suspension Bridges ◽  
Tensile Forces ◽  
Main Cables ◽  
Element Method

Construction of suspension bridges and their structural analysis are challenged by the presence of elements (chains or main cables) capable of large deflections leading to a geometric nonlinearity. For an accurate prediction of the main cable geometry of a suspension bridge, an innovative iterative method is proposed in this article. In the iteration process, hanger tensions and the cable shape are, in turns, used as inputs. The cable shape is analytically predicted with an account of the pylon saddle arc effect, while finite element method is employed to calculate hanger tensions with an account of the combined effects of the cable-hanger-stiffening girder. The cable static equilibrium state is expressed by three coupled nonlinear governing equations, which are solved by their transformation into a form corresponding to the unconstrained optimization problem. The numerical test results for the hanger tensions in an existing suspension bridge were obtained by the proposed iterative method and two conventional ones, namely, the weight distribution and continuous multiple-rigid-support beam methods. The latter two reference methods produced the respective deviations of 10% and 5% for the side hangers, respectively, which resulted in significant errors in the elevations of the suspension points. To obtain more accurate hanger tensile forces, especially for the side hangers, as well as the cable shape, the iterative method proposed in this article is recommended.

Simplified Calculation of Pylon Top Displacement of Multi-Pylon Suspension Bridge

2019 ◽  
Vol 2673 (10) ◽  
pp. 814-825
Author(s):  
Jinquan Zhang ◽  
Pengfei Li ◽  
Wanheng Li ◽  
Yan Mao ◽  
Zhenhua Dong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Model Experiment ◽  
Suspension Bridge ◽  
Suspension Bridges ◽  
The Finite Element Method ◽  
Bridge Testing ◽  
Simplified Calculation ◽  
Simplified Formula ◽  
Element Method

The long-span multi-pylon suspension bridge is the subject of growing interest. Under live load, the longitudinal deflection of the mid-pylon is an important control parameter for a multi-pylon suspension bridge design. It is important to establish a simplified method of calculating pylon deflection for the preliminary design and selection of a multi-pylon suspension bridge. Based on deflection theory and deformation compatibility condition, considering main cable horizontal constraints and the interaction among pylons and girders with the methods of equivalent stiffness and moment distribution, the simplified calculation formulas of pylon displacement at the top for three-, four-, and five-pylon suspension bridges are derived. The validity of the formulas are verified by model experiment, real bridge testing, and finite-element analysis. For a floating system, the error between the simplified formula and the finite element method is less than 10%, and that of the model experiment is within 25%. For a consolidation system, the error between the simplified formula and the finite element method is within 16%, and that of the real bridge testing is less than 11%. As the number of pylons increases, the simplified formulas tend to be less accurate.

scholarly journals A posteriori error estimates for a multi-scale finite-element method

2021 ◽  
Vol 40 (4) ◽  
Author(s):  
Khallih Ahmed Blal ◽  
Brahim Allam ◽  
Zoubida Mghazli
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
A Posteriori Error Estimates ◽  
Numerical Test ◽  
Posteriori Error ◽  
Diffusion Problem ◽  
A Posteriori ◽  
Essential Information ◽  
Multi Scale ◽  
Element Method

AbstractWe are interested in the discretization of a diffusion problem with highly oscillating coefficient, by a multi-scale finite-element method (MsFEM). The objective of this method is to capture the multi-scale structure of the solution via local basis functions which contain the essential information on small scales. In this paper, we perform an a posteriori analysis of this discretization. The main result consists of building error indicators with respect to both small and large meshes used in this method. We present a numerical test in which the experiments are in good coherency with the results of analysis.

An efficient iterative algorithm for the natural convection equations based on finite element method

2018 ◽  
Vol 28 (3) ◽  
pp. 584-605 ◽  
Author(s):  
Lei Wang ◽  
Jian Li ◽  
Pengzhan Huang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Convection ◽  
Iterative Method ◽  
Error Correction ◽  
Computational Time ◽  
Content Type ◽  
Natural Convection Problem ◽  
New Iterative Method ◽  
Element Method

Purpose This paper aims to propose a new highly efficient iterative method based on classical Oseen iteration for the natural convection equations. Design/methodology/approach First, the authors solve the problem by the Oseen iterative scheme based on finite element method, then use the error correction strategy to control the error arising. Findings The new iterative method not only retains the advantage of the Oseen scheme but also saves computational time and iterative step for solving the considered problem. Originality/value In this work, the authors introduce a new iterative method to solve the natural convection equations. The new algorithm consists of the Oseen scheme and the error correction which can control the errors from the iterative step arising for solving the nonlinear problem. Comparing with the classical iterative method, the new scheme requires less iterations and is also capable of solving the natural convection problem at higher Rayleigh number.

scholarly journals Mixed Finite Element Method for Static and Dynamic Contact Problems with Friction and Initial Gaps

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lanhao Zhao ◽  
Zhi Liu ◽  
Tongchun Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Iteration Process ◽  
Mixed Finite Element Method ◽  
Contact Problems ◽  
Dynamic Contact ◽  
Contact Forces ◽  
Stick Slip ◽  
Element Method

A novel mixed finite element method is proposed for static and dynamic contact problems with friction and initial gaps. Based on the characteristic of local nonlinearity for the problem, the system of forces acting on the contactor is divided into two parts: external forces and contact forces. The displacement of structure is chosen as the basic variable and the nodal contact force in contact region under local coordinate system is selected as the iteration variable to confine the nonlinear iteration process in the potential contact surface which is more numerically efficient. In this way, the sophisticated contact nonlinearity is revealed by the variety of the contact forces which are determined by the external load and the contact state stick, slip, or separation. Moreover, in the case of multibody contact problem, the flexibility matrix is symmetric and sparse; thus, the iterative procedure becomes easily carried out and much more economical. In the paper, both the finite element formulations and the iteration process are given in detail for static and dynamic contact problems. Four examples are included to demonstrate the accuracy and applicability of the presented method.

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