[MU [CU [KU f [MUg

In a MDF sytem, a system is discretized into its degrees of freedom. The number of degrees of freedom depend on the number of elements and the degree of freedom for each element. Usually in the case of concrete gravity dams isoparametric plane stress or plane strain are used. These types of elements are used for two dimensional problems. In some cases triangular elements may be used. In both plane stress or plane strain the displacement field is given by the u and v in directions of cartisian x and y axis. In the case of concrete gravity dam, assumption of 2-D analysis is a valid assumption.

In 3-D analysis the simplest case is the case of tetrahedron element. Based on the nature of the problem each node may have 3 different components u, v and w in the direction of X , Y and Z . For more complex type of element we may add rotational degrees of freedom in to each node. Three dimensional analysis of concrete gravity dams requires a large number of DOF.

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