考虑接缝传荷的文克勒地基上矩形薄板的级数解

应用双重正弦级数展开的方法,推演得到了文克勒地基上计入两块矩形板间接缝传荷效应的级数解。假设接缝传递剪力与板间挠度差成正比、传递弯矩与板间转角差成正比,进而分析了单轮和单轴荷载作用在纵缝边缘中部时,接缝传荷效应对板边最大挠度和最大应力的影响规律;通过引入接缝传荷效应系数和接缝极限传荷的两个挠度比及两个应力比,建立了计入接缝传荷效应的板边最大挠度和最大应力的一般式,总结了不同板尺寸、荷载面积尺寸和类型及板材料泊松比对四个接缝影响系数和四个接缝极限传荷的挠度比及应力比的影响规律。结果表明:不同荷载面积下,受荷板接缝边缘最大挠度、最大应力均随弯矩或剪力传荷刚度系数的增大而减小,且应力的变化幅度相较挠度要小。影响系数fV^w(ξV)、fM^w(ξM)、fM^σ(ξM)与荷载圆相对半径(a/l)、相对板长(L/l)和相对板宽(B/l)无关,且单轮荷载与双轮荷载规律相同;而影响系数fV^σ(ξV)与荷载圆相对半径(a/l)有关,与相对板长(L/l)和相对板宽(B/l)无关;挠度比λV^w与荷载圆相对半径、板尺寸(L/l,B/l)及泊松比v无关,恒等于0.5,而λM^w、λV^σ、λM^σ均与荷载相对半径(a/l)、板尺寸(L/l,B/l)及泊松比v有关,且影响因素中荷载面积尺寸的影响最为显著。

The series solution of rectangular thin plate on Winkler foundation considering joint load transfer

By using the method of double sine series expansion,the series solution of the rectangular plate on theWinkler foundation considering the joint loading effect between two rectangular plates is derived.The shear force transmitted by the joint is deemed to be proportional to the difference of deflection between plates and the moment transmitted by the joint is assumed to be proportional to the difference of rotation angle between plates.Furthermore,influence of joint load transfer on the maximum deflection and stress of the plate under uniaxial and single wheel loads is analyzed.By introducing the joint load transfer coefficient,the ultimate deflection ratio and the ultimate stress ratio of the joint load transfer,a general formula for calculating the maximum deflection and maximum stress at the edges of the plate is established.Influences of different plate sizes,load sizes and types,and Poisson’s ratio of plate materials on the joint load transfer coefficients,the ultimate deflection ratio and stress ratio of the joint load transfer are summarized.Results show that under different load areas,the maximum deflection and maximum stress of the joint edge of the loaded plate decrease with the increase of bending moment or shear load stiffness coefficient,and the change range of stress is smaller than that of the deflection.The influence factors fV^w(ξV)、fM^w(ξM)、fM^σ(ξM)are independent of the relative radius of the load circle(a/l),the relative plate length(L/l)and the relative plate width(B/l),and the single wheel load is the same as the two-wheel load rule.The influence factor fV^σ(ξV)is related to the relative radius of the load circle(a/l),and is independent of the relative plate length(L/l)and the relative plate width(B/l).The deflection ratio λV^w is independent of the relative radius of the load circle(a/l),the plate size(L/l,B/l)and Poisson’s ratio v,and is equal to 0.5,while λM^w、λV^σ、λM^σ are all related to the relative radius of the load,the plate size(L/l,B/l)and Poisson’s ratio v,and the influence of load area size is the most significant.