A structure is regular if its model can be represented as a product graph. Regular structures have certain properties that facilitate their optimal static and free vibration analysis. In this paper the concepts of rotational regular and translational regular structures are introduced, and using the well-known dynamic sub-structuring technique a method is proposed to relate the behavior of a translational regular structure to its rotational regular counterpart. It is shown that using the proposed method the analysis of a translational regular structure can be significantly accelerated compared to a direct method of solution.The efficiency of the proposed method in approximating the requested number of natural periods and mode shapes of a translational regular structure is demonstrated through numerical examples. The accuracy of the obtained results is compared to other approximation methods.

Substructuring in the finite element method is a technique that reduces computational cost and memory usage for analysis of complex structures. The efficiency of this technique depends on the number of substructures in different problems. Some subdivisions increase computational cost, but require little memory usage and vice versa. In the present study, the cost functions of computations and memory usage are extracted in terms of number of subdivisions and optimized mathematically. The results are presented in the form of tables which recommend the proper Substructuring for different number of elements. A combined case is also considered which investigates balanced reduction of computational and memory cost for 2D problems. Several numerical examples are analyzed numerically to demonstrate the abilities and efficiency of the proposed computational algorithm for structured and unstructured mesh.

The anchorage of the piles on a stiffer soil layer plays an important role to transmit the loads of the superstructure to the soil. Depending on the pile toe condition, three configurations of piles are considered: floating piles, rested, and anchored piles. To study the effect of the pile toe condition on the dynamic response of pile and pile groups, a three-dimensional finite element modeling of the soil– pile– slab dynamic interaction is presented. The soil and piles are represented as continuum solids and the slab by structural elements. Quiet boundaries are placed at the boundaries of the model to avoid wave reflection. The formulation is based on the Substructuring method. The dynamic response is obtained in terms of the dynamic impedances. In this study the dynamic response of the floating, rested, and anchored piles are analyzed and the group effect is shown. An analysis of the horizontal and vertical pile foundation impedances is presented and the results are compared with different configurations.

In machine dynamics, the tool point frequency response functions (FRFs) are employed to predict the stable machining conditions. A combined analytical-experimental Substructuring procedure is proposed to determine the tool point FRFs usable for different holder-tool configurations. Contact interface of holder-spindle and tool-holder is modeled using translational and rotational springs and dampers spread in the length of contact surface. These joint parameters are defined using finite element method. This enables the analyst to introduce the contact stiffness and damping in more detail taking into account variations of normal pressure in the tool-holder and holder-spindle joints. The dynamic analysis of the holder is done using Timoshenko beam theory by chebyshev method. The tool dynamics is modeled by Euler-Bernoulli beam theory using the method of equivalent diameter. For the purpose of shifting the tool stability lobes to a higher level, tool damping parameter is modified by internal frictional damper and the effect is analyzed by analytical methods and experimental study. New method for continuous dynamic coupling is presented. The method employs the measured spindle-machine FRFs and analytical models of the tool and holder to predict the tool tip FRFs. An experimental case study is provided to demonstrate the applicability of the proposed method.