superposition method
Recently Published Documents

This paper proposes a novel density-based concurrent topology optimization method to support the two-scale design of composite plates for vibration mitigation. To have exceptional damping performance, dynamic compliance of the composite plate is taken as the objective function. The complex stiffness model is used to describe the material damping and accurately consider the variation of structural response due to the change of damping composite material configurations. The mode superposition method is used to calculate the complex frequency response of the composite plates to reduce the heavy computational burden caused by a large number of sample points in the frequency range during each iteration. Both microstructural configurations and macroscopic distribution are optimized in an integrated manner. At the microscale, the damping layer consists of periodic composites with distinct damping and stiffness. The effective properties of the periodic composites are homogenized and then are fed into the complex frequency response analysis at the macroscale. To implement the concurrent topology optimization at two different scales, the design variables are assigned for both macro- and micro-scales. The adjoint sensitivity analysis is presented to compute the derivatives of dynamic compliance of composite plates with respect to the micro and macro design variables. Several numerical examples with different excitation inputs and boundary conditions are presented to confirm the validity of the proposed methodologies. This paper represents a first step towards designing two-scale composite plates with optional dynamic performance under harmonic loading using an inverse design method.

In order to improve the damage feature extraction effect of prefabricated residential building components and improve the structural stability of prefabricated residential components, this paper applies BIM technology to the structural feature analysis of prefabricated residential components. Moreover, this paper adopts the simple superposition method and combines the first strength theory of material mechanics to derive the formula for calculating the cracking torque of prefabricated residential building components under compound torsion. In addition, based on the variable-angle space truss model, this paper uses a simple superposition method to derive the calculation formula for the ultimate torque of composite torsion of fabricated residential building components and applies it to the BIM fabricated residential model. Finally, this paper constructs an intelligent BIM prefabricated residential building construction damage characteristic monitoring system. Through experimental research, it can be seen that the intelligent BIM prefabricated residential building construction damage feature monitoring system proposed in this paper can monitor the damage characteristics of prefabricated residential building construction and can predict the evolution of subsequent building features.

Abstract A new moving Kirchhoff-Love plate element is developed in this work to accurately and efficiently calculate the dynamic response of vehicle-pavement interaction. Since the vehicle can only affect a small region nearby, the wide pavement is reduced to a small reduced plate area around the vehicle. The vehicle loads moving along an arbitrary trajectory is considered, and the arbitrary Lagrangian-Eulerian method is used here for coordinate conversion. The reduced plate area is spatially discretized using the current moving plate element, where its governing equations are derived using Lagrange's equations. The moving plate element is validated by different plate subjected to moving load cases, where the influences of different factors on reduced plate area length of the RBM model are also investigated. Then a vehicle-pavement interaction case with constant and variable speed is analyzed here. The calculation results from the moving plate element are in good agreement with those from the modal superposition method (MSM), and the calculation time with the moving plate element is only one third of that using the MSM. It is also found that the moving load velocity and ground damping have great influences on reduced plate area length of the RBM. The moving plate element is accurate and more efficient than the MSM in calculating the dynamic response of the vehicle-pavement interaction.

Following economic growth in the past three decades, rapid urbanization has caused many pronounced issues, such as spatial scarcity and cultural discontinuity, in Chinese historical and cultural cities. In order to better deal with the diversification of underground space resources, data and information, this study introduces a random forest algorithm and proposes a multi-layer information superposition method. According to the characteristics of different information, starting from qualitative and quantitative aspects, we explore the effective performance of the rational development of underground space resources. Taking Yangzhou City, China, as an example, this paper evaluates the suitability and calculates the development volume of urban underground space. The development capacity, potential value, and comprehensive quality of underground space resources are explored in an attempt to demonstrate the practicality and scientificity of the evaluation method for achieving the developmental goals of urban space reconstruction and historic preservation. On this basis, an underground space scale forecast is carried out to provide decision support for relevant planners, managers, and construction personnel that is conducive to the orderly development of urban space, alleviation of increasing human–land conflicts, and coordination of the protection and development of underground space resources in historical and cultural cities, ultimately promoting sustainable development of cities.

In this paper, the stress superposition method (SSM) is proposed to solve the stress distribution of regular polygon membranes. The stress-solving coefficient and the calculation formula of arbitrary point stress of regular polygon membrane are derived. The accuracy of the SSM for calculating stresses in regular polygonal membranes is verified by comparing the calculation results of the SSM with the finite element simulation results. This article is the first to propose a method to investigate the response of the arch height of the membrane curved edge to the membrane’s mechanical properties while keeping the effective area constant. It is found that the equivalent stress and the second principal stress at the midpoint of the membrane curved edge are effectively increased with the increase of the arch height of the curved edge. The second principal stress at the edge region of the membrane is relatively small, leading to the occurrence of wrinkles. When the stress at the midpoint of the curved edge is equal to that at the center of the membrane, the membrane plane attains the maximum stiffness and reduces the possibility of wrinkling at the edge.

We have analyzed the dynamics of solar wind and interplanetary magnetic field (IMF) parameters during the development of 933 isolated geomagnetic storms, observed over the period from 1964 to 2010. The analysis was carried out using the epoch superposition method at intervals of 48 hrs before and 168 hrs after the moment of Dst minimum. The geomagnetic storms were selected by the type of storm commencement (sudden or gradual) and by intensity (weak, moderate, and strong). The dynamics of the solar wind and IMF parameters was compared with that of the Dst index, which is an indicator of the development of geomagnetic storms. The largest number of storms in the solar activity cycle is shown to occur in the years of minimum average values (close in magnitude to 1) of the solar wind parameter β (β is the ratio of plasma pressure to magnetic pressure). We have revealed that the dynamics of the Dst index is similar to that of the β parameter. The duration of the storm recovery phase follows the characteristic recovery time of the β parameter. We have found out that during the storm main phase the β parameter is close to 1, which reflects the maximum turbulence of solar wind plasma fluctuations. In the recovery phase, β returns to background values β~2‒3.5. We assume that the solar wind plasma turbulence, characterized by the β parameter, can play a significant role in the development of geomagnetic storms.

We have analyzed the dynamics of solar wind and interplanetary magnetic field (IMF) parameters during the development of 933 isolated geomagnetic storms, observed over the period from 1964 to 2010. The analysis was carried out using the epoch superposition method at intervals of 48 hrs before and 168 hrs after the moment of Dst minimum. The geomagnetic storms were selected by the type of storm commencement (sudden or gradual) and by intensity (weak, moderate, and strong). The dynamics of the solar wind and IMF parameters was compared with that of the Dst index, which is an indicator of the development of geomagnetic storms. The largest number of storms in the solar activity cycle is shown to occur in the years of minimum average values (close in magnitude to 1) of the solar wind parameter β (β is the ratio of plasma pressure to magnetic pressure). We have revealed that the dynamics of the Dst index is similar to that of the β parameter. The duration of the storm recovery phase follows the characteristic recovery time of the β parameter. We have found out that during the storm main phase the β parameter is close to 1, which reflects the maximum turbulence of solar wind plasma fluctuations. In the recovery phase, β returns to background values β~2‒3.5. We assume that the solar wind plasma turbulence, characterized by the β parameter, can play a significant role in the development of geomagnetic storms.

It has been for the first time that an analytical solution to the problem of free vibrations of a cantilevered thick orthotropic plate is presented. This problem is quite cumbersome for using the exact methods of the theory of elasticity; therefore, methods based on the variational approach were developed to solve it. The paper suggests using the superposition method to construct a general solution of the vibration equations of a plate in the series form of particular solutions obtained with the help of a variables separation. The particular solutions of one of the coordinates are built in the form of trigonometric functions of a special type (modified trigonometric system). The constructed solution, in contrast to the solutions known in the literature on the basis of the variational approach, accurately satisfies the equations of vibrations. The use of a modified trigonometric system of functions makes it possible to obtain uniform formulas for even and odd vibration shapes and to reduce the quantity of boundary conditions on the plate sides from twelve to nine ones, while five of the nine boundary conditions are also accurately satisfied. The structure of the presented solution on the plate boundary is such that, each of the kinematic or force characteristics of the plate is represented as a sum of two series, i.e. a trigonometric series and a series in hyperbolic functions. Remaining boundary conditions make it possible to obtain an infinite system of linear algebraic equations with respect to the unknown coefficients of the series representing the solution. The convergence of the solution by the reduction method of the infinite system is investigated numerically. Examples of the numerical implementation are given; numerical studies of the spectrum of natural frequencies of the cantilevered thick plate were carried out based on the obtained solution, both with varying elastic characteristics of the material and with varying geometric parameters.

Random road torsional excitation is a key excitation condition for transmission box vibration of tracked vehicles. In order to accurately analyze influences of random road torsional excitation on the vibration characteristics of the transmission box, a calculation method of this excitation for tracked vehicle is proposed based on the random expression of the roughness of standard road surface. Furthermore, random road torsional excitations under different road grades and vehicle speeds are simulated. With the finite element method and modal superposition method, the box body is discretized, and the elastic characteristics of the box body are characterized to explore the dynamics coupling mechanism of gear shafting and the box body. By considering bending-torsional coupling vibration of gear shafting under multi-source excitations, such as the fluctuated torque of engine and dynamic meshing stiffness of gears, dynamic coupling model of gear shafting and box body under random road torsional excitation is established. The dynamic response of the gearbox under random road torsion excitation is obtained by co-simulation with the variable step length Runge-Kutta method. Influences of different road grades, track preload and vehicle speeds on dynamic response characteristics of the gearbox are analyzed. Real vehicle road test scheme is designed to obtain surface acceleration response of the box body at different speeds on the cement road surface. Both test and simulation results are compared and analyzed to verify the accuracy of the simulation method, which provides a theoretical reference for dynamic optimization of the transmission box.