Dynamic Response Solution of Multi-Layered Pavement Structure Under FWD Load Appling the Precise Integration Algorithm

Abstract This paper puts forward a computationally-efficient parallel precise integration algorithm for solving vibration response subjected to time-variable excitation and nonlinearity, especially for non-homogenous dynamic response solution with large-scale degree of freedom. In detail, both of the nonlinear parts and time-varying inputs of the dynamic system are separated from the original dynamic equations and then simulated by employing a piecewise interpolation function within a computing time-step. A novel closed-form iteration formula is presented in conjunction with the block matrix strategy and modified increment-dimensional precise integration technique. Interestingly, the presented approach is essentially a high-accuracy and parallel algorithm, which exhibits a high prediction accuracy without the limitation of matrix inversion, higher-order derivative, periodicity requirement nor cycle oscillation and instability of high-order interpolation. At last, the feasibility and advantage of the proposed method is verified with two numerical examples.

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Research on Dynamic Response of Pavement under Moving Vehicle Loading Using Three Dimensional Finite Element Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.444-445.1197 ◽

2013 ◽

Vol 444-445 ◽

pp. 1197-1203 ◽

Cited By ~ 1

Author(s):

You Xuan Zhao ◽

Yan Jun Qiu ◽

Peng Cao ◽

Chang Fa Ai

Keyword(s):

Finite Element ◽

Dynamic Response ◽

Static Analysis ◽

Vertical Displacement ◽

Numerical Results ◽

Response Analysis ◽

Integration Algorithm ◽

Moving Vehicle ◽

Vehicle Loading ◽

Pavement Structure

To analyze the dynamic response of the pavement structure under moving vehicle loading is always a hot point in pavement engineering. In this paper, the moving vehicle has been simplified as spring-dashpot components and the pavement structure has also been discrete using three-dimension finite element model. Based on Newton iteration and central difference integration algorithm, the static and dynamic coupling reactions between pavement structure and vehicle have also been considered using finite element platform ABAQUS. The numerical results and analytic results can fit very well in static analysis, meanwhile the numerical results and experiment results can fit very well in dynamic analysis. Based on preceding verified numerical model, a few interesting phenomenon have been discovered. The pavement dynamic vertical displacement in upper layer is much higher than the situation in static analysis, because the vertical displacement is superimposed during the dynamic response analysis. Furthermore the vertical fluctuation of the vehicle's bar center exists even the vehicle moving in the initial even pavement, and the inertial forces is the most important reason to induce this behavior. In the last, this paper has proposed a more accurate, fast and concrete evidence to explain the reason that the dynamic response has obvious relationship with the diseases in pavement layer.

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Dynamic Response of Model Pavement Structure

Transportation Engineering Journal of ASCE ◽

10.1061/tpejan.0000264 ◽

1972 ◽

Vol 98 (4) ◽

pp. 1005-1022

Author(s):

Stephen F. Brown ◽

David I. Bush

Keyword(s):

Dynamic Response ◽

Pavement Structure

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Impacts on Dynamic Response of the Pavement Structure Caused by Parameters Variation

Research, Development and Practice in Structural Engineering and Construction ◽

10.3850/978-981-08-7920-4_i-10-0249 ◽

2012 ◽

Author(s):

Bu Jian-Qing ◽

Zhang Da-Ming

Keyword(s):

Dynamic Response ◽

Pavement Structure

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Extension of the Wittrick-Williams Algorithm to Mixed Variable Systems

Journal of Vibration and Acoustics ◽

10.1115/1.2889728 ◽

1997 ◽

Vol 119 (3) ◽

pp. 334-340 ◽

Cited By ~ 32

Author(s):

Zhong Wanxie ◽

F. W. Williams ◽

P. N. Bennett

Keyword(s):

Timoshenko Beam ◽

Stiffness Matrix ◽

Integration Method ◽

Dynamic Stiffness ◽

Integration Algorithm ◽

Precise Integration ◽

Matrix Computations ◽

Precise Integration Method ◽

Count Method ◽

Mixed Variable

A precise integration algorithm has recently been proposed by Zhong (1994) for dynamic stiffness matrix computations, but he did not give a corresponding eigenvalue count method. The Wittrick-Williams algorithm gives an eigenvalue count method for pure displacement formulations, but the precise integration method uses a mixed variable formulation. Therefore the Wittrick-Williams method is extended in this paper to give the eigenvalue count needed by the precise integration method and by other methods involving mixed variable formulations. A simple Timoshenko beam example is included.

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A 3D Direct Vehicle-Pavement Coupling Dynamic Model and Its Application on Analysis of Asphalt Pavement Dynamic Response

Mathematical Problems in Engineering ◽

10.1155/2013/394704 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 3

Author(s):

Peng Cao ◽

Changjun Zhou ◽

Decheng Feng ◽

Youxuan Zhao ◽

Baoshan Huang

Keyword(s):

Finite Element ◽

Dynamic Response ◽

Dynamic Model ◽

Static Analysis ◽

Moving Load ◽

Dynamic Responses ◽

Pavement Surface ◽

Coupling Dynamic ◽

Pavement Structure ◽

Coupling Dynamic Model

Currently dynamic response of the pavement structure is widely studied in pavement engineering. A 3D direct vehicle-pavement coupling dynamic model was developed to describe the pavement dynamic responses in this paper. The moving vehicle was simplified as spring-dashpot components, and the pavement structure was simulated using three-dimension finite element model. Based on Newton iteration and central difference integration algorithm, the static and dynamic coupling reactions between the pavement structure and vehicle were considered using finite element platform ABAQUS. The numerical results fit analytic results very well in static analysis and fit experiment results in dynamic analysis well too. The simulated results indicate that the dynamic pavement surface deflection is much higher than the situation in static analysis, due to the overlapping effect. This phenomenon enhances when vehicle speed increases. A discontinuous zone of shear stress was observed on the base surface between the location under moving load and the location the moving load just passed. It was also found that the vertical fluctuation exists on the vehicle even if there is no roughness on the pavement surface. In general, the developed 3-D direct vehicle-pavement coupling dynamic model was validated to be effective on evaluating pavement dynamic responses.

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Forced Vibration of Surface Foundation on Viscoelastic Isotropic Multi-Layered Stratum

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455415500613 ◽

2016 ◽

Vol 16 (09) ◽

pp. 1550061 ◽

Cited By ~ 9

Author(s):

Lin Chen

Keyword(s):

Dynamic Response ◽

Forced Vibration ◽

Numerical Approach ◽

Contact Forces ◽

Precise Integration ◽

Irregular Shapes ◽

Layered Stratum ◽

Surface Foundation ◽

Soil Foundation ◽

Impedance Functions

A numerical approach is presented for analyzing the forced vibration of a rigid surface foundation. In the analysis, the foundation is discretized into a number of sub square-elements. The dynamic response within each sub-element is described by the Green’s function, which is obtained by the Fourier–Bessel transform and the precise integration method (PIM). Then, a system of linear algebraic equation in terms of the contact forces within each sub-element is derived, which leads to the desired dynamic impedance functions of the foundation. Numerical results are obtained for the foundation not only with a simple geometry, such as circular one, but also with irregular shapes. Comparisons between the results obtained by the proposed approach and the thin layered method are made, for which good agreement is achieved. Also, parametric studies are performed on the dynamic response of the foundation, considering the effects of the material damping, stratum depth, Poisson’s ratio and the contact condition of the soil–foundation interface. Several conclusions are drawn concerning the significance of each parameter. Further application of the method can be easily extended to the analysis of a foundation on a viscoelastic anisotropic multi-layered stratum because no further complexity is introduced except the constitutive matrix needs to be modified.

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An Accurate and Efficient Method for Dynamic Analysis of Two-Dimensional Periodic Structures

International Journal of Applied Mechanics ◽

10.1142/s1758825116500137 ◽

2016 ◽

Vol 08 (02) ◽

pp. 1650013 ◽

Cited By ~ 3

Author(s):

Q. Gao ◽

H. W. Zhang ◽

W. X. Zhong ◽

W. P. Howson ◽

F. W. Williams

Keyword(s):

Dynamic Response ◽

Efficient Method ◽

Algebraic Structure ◽

Integration Method ◽

Periodic Structures ◽

Computational Effort ◽

Two Dimensional ◽

Great Efficiency ◽

Energy Propagation ◽

Precise Integration

In this paper, an accurate and efficient method is presented for analyzing the dynamic response of two-dimensional (2D) periodic structures. The algebraic structure of the corresponding matrix exponential is analyzed and, based on its special structure, an accurate and efficient method for its computation is proposed. Accuracy is maintained using the precise integration method (PIM), and great efficiency is achieved in the computational effort using the periodic properties of the structure and the energy propagation features of the dynamic system. The proposed method is compared with the conventional Newmark and Runge–Kutta (R–K) methods, and it is shown to be accurate, efficient and extremely frugal in its memory requirements.

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