In the theory of elastic thin plates, the bending of a rectangular plate on the elastic foundation is also a difficult problem. This paper provides a rigorous solution by the method of superposition. It satisfies the ...In the theory of elastic thin plates, the bending of a rectangular plate on the elastic foundation is also a difficult problem. This paper provides a rigorous solution by the method of superposition. It satisfies the differential eguation, the boundary conditions of the edges and the free corners. Thus we are led to a system of infinite simultaneous eguations. The problem solved is for a plate with a concentrated load at its center. The reactive forces from the foundation should be made to be in equilibrium with the concentrated force to see whether our calculation is correct or not.展开更多
In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of ser...In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot bedetermined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.展开更多
This study uses a recently proposed algorithm for consideration of soil sounding locations in the bearing capacity estimations of spatially variable soil for rectangular footings.The objective of the study is to asses...This study uses a recently proposed algorithm for consideration of soil sounding locations in the bearing capacity estimations of spatially variable soil for rectangular footings.The objective of the study is to assess the possibility of indicating general guidelines for optimal soil sounding locations in the case of two soundings and rectangular footings.The possibility of proposing such general guidelines would be extremely valuable from the engineering practice point of view.Moreover,it would be promising for future studies concerning more complex foundation arrangements.For this reason,numerous scenarios are analyzed for a variety of vertical and horizontal fluctuation scales and a variety of rectangular foundation lengths.For generality of the results,two correlation structures are considered,i.e.the Gaussian and the Markovian ones.The optimal sounding location results are discussed.The observations indicate that,for a specified vertical fluctuation scale,all optimal borehole locations in dimensionless coordinates form a curve.This phenomenon can be utilized in practical applications.The potential applications of the obtained results and the directions for future studies in this area are also discussed.展开更多
文摘In the theory of elastic thin plates, the bending of a rectangular plate on the elastic foundation is also a difficult problem. This paper provides a rigorous solution by the method of superposition. It satisfies the differential eguation, the boundary conditions of the edges and the free corners. Thus we are led to a system of infinite simultaneous eguations. The problem solved is for a plate with a concentrated load at its center. The reactive forces from the foundation should be made to be in equilibrium with the concentrated force to see whether our calculation is correct or not.
文摘In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot bedetermined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.
文摘This study uses a recently proposed algorithm for consideration of soil sounding locations in the bearing capacity estimations of spatially variable soil for rectangular footings.The objective of the study is to assess the possibility of indicating general guidelines for optimal soil sounding locations in the case of two soundings and rectangular footings.The possibility of proposing such general guidelines would be extremely valuable from the engineering practice point of view.Moreover,it would be promising for future studies concerning more complex foundation arrangements.For this reason,numerous scenarios are analyzed for a variety of vertical and horizontal fluctuation scales and a variety of rectangular foundation lengths.For generality of the results,two correlation structures are considered,i.e.the Gaussian and the Markovian ones.The optimal sounding location results are discussed.The observations indicate that,for a specified vertical fluctuation scale,all optimal borehole locations in dimensionless coordinates form a curve.This phenomenon can be utilized in practical applications.The potential applications of the obtained results and the directions for future studies in this area are also discussed.
