大底盘多塔楼连体结构的振动计算和动力特性

用沿高度方向分段连续化的方法,对底部为大底盘、上部为多塔楼、塔楼间带连廊的高层建筑结构,建立一个分段连续的串并联振动模型,导出其水平振动的弯扭耦连振动微分方程组,用常微分方程求解器COLSYS求解其自振频率及相应的振型.讨论了连廊不同刚度时的振动特性.为复杂结构提供了一种可用的动力计算简化方法.     

变截面高层筒体结构的水平振动

本文用有限元线法对变截面的高层筒体结构的动力特性进行分析.先用分段连续化方法将实际框筒结构等效为变截面的正交各向异性折板结构;将结构沿一个方向(横向)半离散化,取结线位移为基本未知函数,通过势能驻值原理,建立半解析的振动微分方程组;然后用常微分方程求解器COLSYS求解频率和振型.为多维结构的振动分析提供了一个半解析的新解法.     

高层建筑自由振动近似计算

对于高层结构自由振动我们感兴趣的是其中心轴的振动情况。因此我们可以将其简化为一个与该结构具有相同刚度,质量分布的Timoshenko梁来进行研究。根据哈密顿原理推导出控制方程和边界条件,然后用常微分求解器进行求解。     

变截面框架-剪力墙-薄壁筒斜交结构考虑竖向荷载作用时的弯扭耦连振动

用沿高度方向分段连续化的方法,对沿高度方向为阶形变截面、在平面内为任意斜向布置的框架-剪力墙-薄壁筒协同工作体系,考虑竖向荷载作用的影响,建立了弯扭耦连的振动方程,用常微分方程求解器COLSYS求解了自振频率及相应的振型.讨论了高层建筑结构竖向荷载对水平振动的影响.     

高层建筑结构考虑楼板变形时水平振动的常微分方程求解器解法

本文对需考虑楼板变形的框架－剪力墙结构的水平振动建立一个连续化的并联模型，导出其振动方程组，用常微分方程求解器求解其自振频率和相应的振型。为抗震计算提供一个简便可行的算法。     

薄壁杆系结构自由振动精确求解的动力刚度法

将动力刚度法应用于薄壁杆系结构自由振动的分析.采用常微分方程求解器COLSYS求解薄壁杆件单元动力刚度所满足的常微分方程边值问题获得单元动力刚度的数值精确解,基于COLSYS求解单元动力刚度的网格采用Wittrick-Williams算法获得单元固端频率的计数,调用COLSYS求解单元动力刚度对频率的导数所满足的常微分方程边值问题获得其数值精确解.由此建立起薄壁杆系结构自由振动精确求解的导护型牛顿法,求得精确的频率和振型.本文数值算法的计算结果与文献以及ANSYS软件的计算结果吻合很好,表明本文方法准确、可靠、有效,可进一步推广应用于其他复杂结构自由振动的分析.     

核心单筒式悬挂结构的振动刚度矩阵

核心单筒式悬挂结构的振动是一个非常复杂的问题,这里用一个简单而有效的方法推导了其振动刚度矩阵,为实际工程计算提供参考.     

大底盘多塔楼连体结构的受力分析

用沿高度方向分段连续化的方法,对底部为大底盘、上部为多塔楼、塔楼间带连廊的高层建筑结构,建立一个分段连续的串并联模型,导出其在水平荷载作用下的平衡微分方程组.用常微分方程求解器COLSYS求解其位移和内力.为复杂结构设计提供了一种简化的算法.     

温度变化对正交索网结构非线性振动的影响

正交索网结构作为屋盖支承体系有着广泛的应用,属于一种柔性结构,对外荷载的作用比较敏感.非线性自振特性的研究对于正交索网结构在风荷载作用下的响应分析具有重要意义.本文考虑温度变化及几何非线性影响,采用连续化理论导出了正交索网结构非线性振动方程.通过Galerkin原理,将偏微分方程转化为常微分方程,并采用改进的L-P法对常微分方程进行了求解.结合算例讨论分析了温度变化、振幅等因素对正交索网结构非线性振动的影响.算例表明,正交索网结构固有频率随着温度的升高而减小,自振频率密集,具有较强的非线性,其自振频率随着振幅发生变化,其非线性振动呈现"硬弹簧"特性,正交索网结构的非线性自振频率高于线性频率.     

履带起重机超起工况臂架结构瞬态动力学分析

履带起重机的主要工作构件是臂架，针对履带起重机超起工况臂架结构，本文首先通过集中质量法将臂架结构简化为二质量二自由度的离散体模型，用柔度法建立运动微分方程，求解模型的基频和第二阶固有频率及对应振型，通过理论推导得到变幅拉板视为线弹性体时的计算公式，通过基于C#语言VisualStudio集成开发环境的响应求解程序解得臂架结构的位移响应和速度响应。结果表明，臂架结构的固有频率较低，属于低频振动，应重点考察其低频振动特性，基于振型结果可知臂架结构按前两阶固有频率振动时的形态变化，响应结果符合工况过程，最大位移满足静力学理论值，为其他履带起重机超起工况瞬态动力学分析提供了思路参考。     

薄壁箱粱桥自由振动的半解析分析

以常微分方程求解器为工具,利用半解析方法对薄壁简支箱梁桥的自由振动进行了分析计算,建立了具有连续分布质量和刚度的三维连续化动力分析模型,也就是将箱梁简化为一个带凸缘的薄壁筒组合体。计算结果表明,分析模型是合理的、可行的,从而为认识此类结构的动力特性提供了一种新的途径和方法。     

A consistent modelling methodology for secondary settling tanks in wastewater treatment

The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solid-liquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models.     

Collision detection strategies for virtual construction simulation

This research aims at developing a simple and efficient collision detection method to support the rendering of a virtual construction scenario in real time. To expedite the collision detection algorithm, we approximated construction machineries and structural elements on a construction site by using spheres and cylinders. By modeling the objects using outer boundaries, the computational cost for collision detection can be significantly reduced. Using the outer boundary also provides the benefit of ensuring a conservative result (i.e. towards the safer side). VC-COLLIDE, the collision detection algorithm developed in this research, has also been presented. VC-COLLIDE has been implemented and tested by using three typical construction scenarios: small building scenarios (683 objects), large building scenarios (2143 objects) and tall building scenarios (2612 objects). The test results indicate that VC-COLLIDE can complete all the collision checks within 1/20th of a second, the upper bound of real-time refresh time in the three testing environments. We also compared VC-COLLIDE with the collision detection function in Open Dynamic Engine (ODE), a widely used physics engine for real-time visualization. Because VC-COLLIDE is designed specifically for using in a virtual construction scenario, its computational performance is significantly better than ODE.     

Bending analysis of thin annular sector plates using extended Kantorovich method

Highly accurate approximate closed-form solution is presented for bending of thin sector plates with clamped edges subjected to uniform and non-uniform loading using the extended Kantorovich method (EKM). Successive application of EKM converts the governing equation which is a forth-order partial differential equation (PDE) to two separate ordinary differential equations (ODE) in terms of r and θ. The obtained ODE systems are then solved iteratively with very fast convergence. In every iteration, exact closed-form solutions are obtained for both ODE systems. It is shown that the method provides sufficiently accurate results not only for deflections but also for stress components. Comparison of the deflection and stresses at various points of the plate shows very good agreement with results of other analytical and numerical analyses.     

大底盘多塔楼结构的整体稳定计算

用沿高度方向分段连续化的方法,对底部为大底盘、上部为多塔楼的高层建筑结构建立了整体的稳定方程,用常微分方程求解器COLSYS求解,为这种复杂的高层建筑结构的整体稳定计算提供了一种简化算法.     

A Bistable Reaction in Autocatalytic Chemical Reaction

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