SUMMARYIn the paper a mathematical formulation for embedding reinforcements in 3D brick concrete elements is presented. The computational aspects and the implementation process of the model have been discussed. The proposed algorithm may be implemented in 3D finite element programs for stress analysis of reinforced concrete structures.KEY WORDS finite element analysis; reinforced concrete element; embedded reinforcement; stress analysis; brick element

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SUMMARYIn this paper a new and innovative method for computation of longitudinal dynamic characteristics of multi-cracked bars is proposed. Cracks are modeled by equivalent axial springs with specified flexibility. Making use of the Heaviside step function and Dirac's delta distribution, a single governing equation for the whole bar is developed. The governing equation is an ordinary differential equation. With the help of Laplace Transform, a general analytical solution in terms of several unknown coefficients is determined. Boundary conditions are then used to determine the analytical solution for specific problems. Making use of the proposed governing equation a new finite element formulation is derived. In this formulation the effect of cracks is considered by adding an equivalent mass matrix to the element mass matrix. Through numerical study, the accuracy, efficiency and robustness of the work is verified.

Construction of a probability function for a given random data is the main theme of several branches of human knowledge, where it is an active area of study. In spite of great developments, the solution needs extensive effort and the results contain epistemic uncertainty. In this study, making use of the logical reasoning and concise mathematical logics, a method called the change of state philosophy, which is digested in the Persian curves, is derived. The Persian curves that have the necessary and sufficient condition for a probability function, are explicitly derived, via the ordinates of four specific points on the random data. The proposed Persian curves are free of epistemic uncertainty and their flexibility provide the possibility for the insertion of the expert's will. The work is validated via concise logical formulation and comparison of the results with those of the others.