文克勒地基板极限承载力的弹塑解

ElasticPlastic Solution to Ultimate Bearing Capacity of Plate on Winkler Foundation

摘要:

将圆形均布荷载作用下的文克勒地基板出现环状裂缝时的板划分为二个区域，环内屈服区仍采用刚塑性假设，而环外弹性区采用线弹性假设，进而推导得到了文克勒地基上板极限承载力的弹塑性解，其中，环状裂缝出现位置由板承载力最小化条件求出，从而弥补了现有刚塑性理论解中不能确定环状裂缝出现位置的缺陷，使理论解更完备且具有良好的拓展性.分析结果表明，梅依尔霍夫的地基板承载力的解偏大且在圆形均布荷载相对半径ρa=2.925时发散，在ρa=0.09~0.70范围时，梅氏解偏大6%~10%.最后，为简便使用给出了弹塑性解的板极限承载力系数φE回归式.

Abstract:

The plate on Winkler foundation with circumferential crack was divided into two areas under circular uniformly distributed load. Rigidplastic hypothesis was used inside the circumferential crack and linearelastic hypothesis was used outside it. Then, the elasticplastic solution to ultimate bearing capacity of plate on Winkler foundation was given. Besides, the position of annular crack was found on the condition of minimal ultimate bearing capacity, which could compensate for the defects that the location of the annular cracks could not be solved using the existing rigidplastic theory. It is more complete and has good expansibility. The result shows that the Meyerhof’s solution to ultimate bearing capacity of plate is larger and divergent when the relatively radius of circular uniformly distributed load is 2.925. The Meyerhof’s solution is 6% to 10% larger when the relatively radius of circular uniformly distributed load is between 0.09 and 0.7. Finally, a more convenient regression formula of ultimate bearing capacity of plate coefficient was proposed.