3-D Modeling And Finite Analysis Of The Cardioid Double-curvature Arch Dam

With the rapid development of economy in our country, the demand for electricity invarious industries of our country is becoming more and more. As a kind of sustainabledevelopment energy strategy, hydropower has a huge contribution to the country’seconomic and social development, however, hydropower resources as a potential healthenergy, has been developed in our country far less than the degree of European countries.So exploitation and utilization of the abundant hydropower resources in our countrybecome an important task in water conservancy and hydropower construction. The archdam as a safe and stable, economical and beautiful dam type plays an important role inmodern water conservancy and hydropower construction, especially in the canyonswhich have better geological and topographical conditions the arch dam plays anirreplaceable role. The arch dam construction has a long history, and the line type of archdam developed from arc arch dam in the beginning, to parabolic arch dam, oval arch dam,double-curvature arch dam, cubic spline curve arch dam, logarithmic spiral curve archdam and hybrid curve arch dam in the later development. It seems like that the design andresearch of line type in arch dam have matured, but in fact it has been limited to theexisting arch dam linear research, so if there is no breakthrough and innovation, theresearch of line type in arch dam will eventually stagnate. Meanwhile the future trends ofarch dam are in the face of more unfavorable geological and topographical conditions, sothis will require more line types to compare, and the study of a new line type is crucial forthe arch dam’s development. In this background, this paper in the first time proposescardioid as a new line type for the arch dam. This paper taking cardioid as the startingpoint of innovation and the object of study, deduced cardioid mathematical equations asthe central axis of arch ring arch dam, established the mathematical model of the cardioiddouble-curvature arch dam, and realized the cardioid double-curvature arch dam’sintelligent drawing program of the three-dimensional entity model combining AutoCADwith C language programming. And this paper introduced the related principle of thefinite element method and related applications in ANSYS software, designed parametricmodeling program of the cardioid double-curvature arch dam in ANSYS, and had thesimulation of cardioid double-curvature arch dam under special load condition inANSYS. Based on the finite element analysis results of stress, cardioid as a new line type of arch ring proved rationality, and through comparing with parabolicdouble-curvature arch dam, it was concluded that the advantages and disadvantages ofcardioid double-curvature arch dam. The cardioid double-curvature arch dam puttingforward and shape modeling will provide theoretical basis and the scientific basis for thenew arch dam research and development.This paper mainly focused on the cardioid,but its rectangular coordinate systemequation was very complex for arch dam modeling, but through the combining withcardioid polar equation, we found the breakthrough point in cardioid arch dam modeling.Therefore, according to the cardioid polar equation we deduced cardioid mathematicalequation as central axis of arch ring firstly, then established the mathematical relationshipbetween polar angle of cardioid and central angle of arch dam, and combining with bodyshape parameters characteristics of arch dam, and setting up the initial half central angle,we can get the parameters of cardioid itself. According to the parameters of cardioid wejust got, we can establish cardioid mathematical equations as the central axis of arch ringand as upstream and downstream line of arch ring. Combining with crown cantilevermathematical equations in the design specifications, and using C language programmingdesign, we realized the cardioid double-curvature arch dam calculating and drawing ofcoordinates, curve fitting, surface creating and arch dam’s body shape modeling. Uponcompletion of the preliminary arch dam modeling, it can be analyzed in ANSYS for stressanalysis, and according to the finite element analysis results of stress, we can adjustparameters where it does not conform to the design specification, finally we can getcardioid double-curvature arch dam available to conform to the design specification. Thispaper laid the foundation for the optimization design of the cardioid double-curvaturearch dam for the future.