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Mathematical models of mechanical characteristics of multilayered PCB

DOI 10.18127/j00338486-201906(8)-14


Al-Araji Zainab Hussam Mosa – Undergraduate, Department Radio Equipment Engineering and Manufacturing, Voronezh State Technical University

The reliability of electronic modules is based both on the reliability of individual components and the reliability of the supporting structure of the printed circuit board. In modern devices, the printed circuit board is a rather complex multi-layer structure that is subjected to vibrations, shocks and static loads. For the analysis of the mechanical properties of printed circuit boards, computer simulation using the finite element method is widely used. When modeling, there is an acute question of clarifying the accuracy. One way to determine this parameter is to compare the results with the results of analytical calculations. The article provides information about the mathematical models of multilayer printed circuit boards, which can be taken as the basis for analytical calculations.
When modeling the mechanical properties of structures of radioelectronic devices, there is an acute problem of the accuracy of the most frequently used finite element method (FEM). This can be found out by comparing the results of analysis on a computer with the results of a real experiment on a vibratory stand. However, this method is rather laborious and expensive, as it takes a lot of time. The accuracy of the simulation can also be assessed by comparing the mechanical characteristics of the structure with an analytical calculation. However, this method is applicable, only, as a rule, to simple objects for which it is possible to obtain an analytical model. Mathematical models of objects of radioelectronic devices of different levels of unbundling with a simple form are presented by a number of Russian and foreign researchers, however, models of multilayer boards are poorly lit there.
As an example, a rectangular board with rigidly fixed edges, in which the load is applied to a central point, is considered. Expressions for calculating the stiffness of a seven-layer printed circuit board, as well as determining the equivalent stiffness and natural frequency are given. When designing electronic modules with multilayer printed circuit boards, computer analysis based on the finite element method is widely used to analyze their vibration properties. Comparison of results with results based on the analytical method can be used to assess the accuracy of modeling. In addition, analytical calculations are more applicable to simple designs, and they can also be used as preliminary. For this, the proposed mathematical models of multilayer printed circuit boards can be used.

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