Curved Shell Analysis And Arch Dam Calculation Based On Exact Geometry

Curved shells are widely used in practical engineering.The Finite Element Method(FEM)is usually used in the mechanical analysis of curved shells.Because the governing equations of the curved shell is complex,they are seldom used to deduce the numerical calculation formula by using the governing equations.So it is usually to discrete the curved shell into several plate elements,which is easy to introduce the geometric error.And FEM also has the following problem: the thin plate element has the difficulty of constructing approximation functions keeping first derivatives continuous,and the thick shell element has various self locking problems.In this paper,a Numerical Manifold Method(NMM)based on independent cover is used to make full use of the flexibility of the series in the independent cover,to reflect the deformation characteristics and fundamental assumptions of the shell.At the same time,the geometric change of the middle surface of the shell is reflected in the strain calculation,to implement exact geometric analysis of the shell.Therefore,a new method for the analysis of curved shells has been formed.The characteristics of this method are:(1)The fundamental assumption of the shell deformation can be simulated in the solid analysis,which only needs to make some items in the polynomial cover functions not involved in the calculation.Thus the complicated procedures of deriving the governing equation of the curved shell and the formula of the numerical analysis are totally avoided.(2)The exact geometry of the curved shell can be achieved by introducing the local coordinate system on the middle surface of the curved shell and calculating the derivatives of the local coordinate and the direction cosines with respect to the global coordinates.Thus the geometric error caused by splicing plate elements to form curved shell is avoided.(3)Only the continuity of the approximate function is required,so that the requirement of continous first-order derivatives in the approximation function can be avoided.(4)The setting of cover functions automatically avoids the problem of shearlocking and membrane locking.With the middle plane and the thickness described by polynomials,the above method is applied to the calculation of arch dam.Only by using dozens of independent covers and three order polynomials,the results of displacement and stress,which are very close to the solutions using very fine meshes of FEM,can be obtained.Meanwhile,it also shows the convenience in the modeling.Only the shape parameters of the arch dam are input,and the rectangular grids is divided on the projection plane.As a contrast,the space positions of the arch dam need to be calculated for dividing meshes in FEM.Therefore,this method also provides a new way for the calculation of arch dams.