The mechanical discrete or continuum structures are actually of great importance in the application field of contemporary modern industry. However, during their life time these structures are often subjected to considerable external stresses or to high amplitudes of vibrations which can cause them large deformations and internal stresses which can cause them internal cracking or even their total destruction. In order to avoid these types of problems, the concept of static and dynamic analysis of these structures is recommended, and due to the complexity of their shape and size, the finite element method is the most used. The latter is currently recognized as a very powerful technique for the static and dynamic analysis of discrete or continuous structures of complicated form applied in the field of mechanics, aeronautics, civil engineering, maritime or robotics. Consequently, the calculation and dimensioning of these mechanical systems by the finite element method plays an important role at the service of the industry for possible sizing and prediction of their lifetime. Our work consists of static and dynamic analysis of two-dimensional discrete and continuous mechanical systems using the finite element method based on the main elements of bars, beams and plates, under the effect of external excitations with different boundary conditions. The discrete structures considered are two-dimensional in metallic framework interconnected to the nodes by welding, riveting or bolted under various boundary conditions. Their elements are modeled comparatively by bar elements and beam elements, while for continuous structures the elements are rectangular thin plates with different boundary conditions. The excitation forces are based on periodic, random or impulsive forces and a numerical solution by development of a program to describe the behavior of these structures is realized. The mass and stiffness matrices of all the structures are determined respectively by assembling the bars, beam and plate elements based on the kinetic and deformation energy for each element. The displacements, the node reactions and the axial forces in all the elements as well as the transverse stresses and the eigenvalues of the structures under different boundary conditions were also calculated and good results were obtained compared to those obtained using other software already existing. In fact, analysis using the finite element method will allow the proper dimensioning and design of complex industrial mechanical structures according to different boundary conditions, their internal loading and their vibratory level.
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We have been accustomed to traditional materials such as wood, leather, wool... and have known the revolution of plastics and composites materials. Recently, we have known other innovations: these of smart materials able to change the shape as the piezoelectric materials. This work deals with the electro-mechanical modeling of these structures by the finite element method. It consists on to model and to simulate deformations in a square aluminum plate subjected to an electric field. This is achieved by using PZT piezoelectric transducers that have such particularity to deform under the influence of an electric field. The study of the deformed aluminum plates equipped with a PZT patch is considered and these types of materials are commonly used in aeronautics and astronautics, which is the context of our study. We have clearly shown the effect of the electromechanical properties of different piezoelectric materials, the transverse piezoelectric coefficient d31 and the longitudinal piezoelectric coefficient d33 of PZT patch on the final response of the intelligent structure.
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