Geodesic
A new approach for development of finite elements
Theoretical and applied mechanics, Tome 8 (1982) no. 1, p. 111 .

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The potential energy in the element is replaced by the work of forces on the boundaries of the element (6). Thus, additional terms are included that are not contained in the potential energy, and an improved stiffness matrix is obtained. The deformation function in the element must not be compatiable. Based on this function, the forces at the boundaries of the element are determined (Fig. 3.). The element can be viewed as if it were connected by knots with beams. These forces are transferred at the nodal points and the coefficients of the stiffness matrix are obtained. The physical significance of the problem must always be kept in mind. It is recommended to use the single strain theorem and the single force. Thus, for some stiffness coefficients, $K_{ij}\neq K_{ji}$ is obtained. The results obtained by the development elements of the proposed approach are the best, and they can always be taken with confidence. Therefore, it is necessary to obtain the best elements according to the proposed concept for solving all types of problems. This is especially important for iso-parametric elements. 
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     author = {Apostol M. Poceski},
     title = {A new approach for development of finite elements},
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     number = {1},
     year = {1982},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAM_1982_8_1_a12/}
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Apostol M. Poceski. A new approach for development of finite elements. Theoretical and applied mechanics, Tome 8 (1982) no. 1, p. 111 . http://geodesic.mathdoc.fr/item/TAM_1982_8_1_a12/