Abstract: Develops a general five‐axle vehicle model to study the dynamic interactions between the moving mass and the bridge structural components. Two‐axle, three‐axle, or four‐axle sprung loads, and the limiting load conditions such as a moving constant force, a moving alternating force, a moving unsprung mass, and combinations thereof, can be treated as special cases of the more general case presented. Further, its integration with the versatile finite element modelling has enhanced the practical applicability of such a theoretical development. The physical characteristics of the bridge and the vehicle, such as the bridge geometry, mechanical properties, profile of the road surface, the vehicle parameters including the distance between axles, leaf springs suspension and the total weight, are considered explicitly in the present model. The dynamic equations of equilibrium in time are integrated using the Newmark integration scheme. Verifies the accuracy of the algorithm by comparing the numerical results obtained from the present formulation with the experimental results.

Abstract: A finite element model for investigating damage evolution in brittle matrix composites was developed. This modeling is based on an axisymmetric unit cell composed of a fiber and its surrounding matrix. The unit cell was discretized into linearly elastic elements for the fiber and the matrix and cohesive elements which allow cracking in the matrix, fiber-matrix interface, and fiber. The cohesive elements failed according to critical stress and critical energy release rate criteria (in shear and/or in tension). The tension and shear aspects of failure were uncoupled. In order to obtain converged solutions for the axisymmetric composite unit cell problem, inertia and viscous damping were added to the formulation, and the resulting dynamic problem was solved implicitly using the Newmark Method. Parametric studies of the interface toughness and strength and the matrix toughness were performed. Details of the propagation of matrix cracks and the initiation of debonds were also observed.

Abstract: In this paper, the second-order-accurate non-dissipative Newmark method is modified to third-order-accurate with controllable dissipation by using complex time steps. Among these algorithms, the asymptotic annihilating algorithm and the non-dissipative algorithm are found to be the first sub-diagonal (1,2) and diagonal (2,2) Pade approximations, respectively. The non-dissipative algorithm is therefore fourth-order-accurate. The stability properties and errors for algorithms with other dissipations are between these two algorithms. The spectral radii, the algorithmic damping ratios and the relative period errors for the present third-order complex-time-step algorithms are compared favourably with other algorithms.

Abstract: In this paper a traveling wave model for describing the lightning stroke is developed. The finite element method is used to derive the element equations and one-dimensional linear elements are used to discretize the field region. The implicit Newmark time integration algorithm is employed to obtain the recurrence formulas for the solution of field variables at each time step. Numerical examples are included and illustrated.

Abstract: To be efficient, the simulation of multibody system dynamics requires fast and robust numerical algorithms for the time integration of the motion equations usually described by Differential Algebraic Equations (DAEs). Firstly, multistep schemes especially built up for second-order differential equations are developed. Some of them exhibit superior accuracy and stability properties than standard schemes for first-order equations. However, if unconditional stability is required, one must be satisfied with second-order accurate methods, like one-step schemes from the Newmark family.

Abstract: A simple fully discrete finite element method is proposed to solve the time-dependent nonlinear Lawrence-Doniach model for layered superconductors. Numerical stability and optimal energy-norm error estimates are established for the proposed numerical method.

Abstract: The development of aircraft composite propeller is necessarily required because recently changing metal propeller to composite propeller is a global tendency due to the improvement of composite manufacture technique and good characteristics of composite materials. The composite propeller blade must be safely designed about static and dynamic loads. The structural stability of composite propeller blades in this study was analyzed by the Finite Element Method. When the static load was acted on the composite propeller, linear and nonlinear analysis was performed with the three different types of blade structure. In order to analyze the problem of the dynamic impact load acted on the blade of shell-spar-foam structure by bird strike, Newmark method was used for linear direct transient analysis. And the Campbell diagram was drawn as the result of eigenvalue problem analysis about the composite propeller. The Natural frequencies of the shell-spar-foam blade were compared with the forced frequencies by engine rotational speed and it was found that the resonance phenomenon did not occurr in the blade. The results of the above structural analysis will be used as technical data fer the design optimization of composite propeller blade.

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Abstract: : This technical report summarizes an assessment of the accuracy of six numerical step by step procedures used in computational structural dynamics. The results provide quantitative guidance on how the accuracy of these procedures is affected by the time step and the ground motion frequency characteristics. The six procedures evaluated in this study are representative of the different types of numerical algorithms used to compute the dynamic structural response to a time dependent loading. The time dependent loading is expressed in terms of a ground acceleration time history. The dynamic structural response for each structural model is characterized by the computed response time histories of accelerations, velocities, and displacements. Using single-degree-of-freedom (SDOF) models with natural periods assigned based on consideration of the important modal periods of hydraulic structures, an evaluation is made of the accuracy of the computed responses at regular time increments during ground shaking. A ground acceleration applied at the base of an SDOF system is equivalent to a fixed base SDOF system with the forcing fimction applied to the mass. The results show a correlation between the accuracy of the six numerical step-by-step procedures with the time step value and frequency characteristics of the ground motion used in the analyses. The six algorithms included in this study are the Newmark beta method (with values of gamma and beta that correspond to the linear acceleration method), the Wilson theta Method, the Central Difference Method, the 4th order Runge-Kutta method, Duhamel's integral solved in a piecewise exact fashion, and the piecewise exact method applied directly.

Abstract: This paper describes a computationally efficient procedure for simulating large overall motions of beams undergoing large deformations. The beam is modeled for this purpose as an assemblage of rigid rods connected by rotational springs. An order-n formulation for loads as well as motions is given, and the results compare well with those given by a nonlinear finite element code. An adaptation of the Newmark integration to the order-n equations is considered, but the simulation results indicate that the rigid segment order-n formulation requires a higher order integrator to give comparable levels of accuracy with a finite element formulation.