The liquid storage tank is a combination structure of the shells, In general, it consists of shallow spherical shell, cylindrical shell and conical shell on the elastic foundation. As regards the analyses of shallow spherical shell and cylindrical shell, there had been a lot of discussion. But, the bending problem of conical shells on the elastic foundation, especially accurate solution, is not solved. So, it is important significance for calculation of liquid storage tank to obtain the solution of conical shells on the elastic foundation.

A principal contribution of this paper is to give a systematic analyses method of conical shell o the elastic foundation. Here, the displacement solution method of the axisymmetric bending of conical shell on the elastic foundation is presented. From the differential equations in displacement form of conical shells and by introducing a displacement function, U(s), the differential equations are changed into a six-order soluble differential equation with variable coefficients. As the special cases of this paper, the displacement function introduced by V.Z. Vlasov in circular cylindrical Shell, the basic equation of the cylindrical shell on the elastic foundation and that of the circular plate on the elastic foundation are directly derived out.

Under the loads arbitrarily distributed along the meridian and boundary conditions, the accurate solution of the six-order differential equation is obtained in power series form. Simultaneously, for the sake of application of the theory presented in this paper, the detailed numerical results are given and some tables of flexible coefficient are calculated, which can be used to analyses the combination structures of conical shells on the elastic foundation. In addition to, the accurate solution presented in this paper can be used to judge accuracy of numerical solution and approximate solution of the same kind of the problem.

As a valuable application of this theory, the liquid storage tank is calculated.

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