DOI: 10.14489/td.2017.07.pp.034-039

Budadin O. N., Kaledin V. O., Kozelskaya S. O., Vyachkina Ye. A., Gilyova A. Ye.
NUMERICAL SCHEME FOR APPROXIMATE CALCULATION OF IMPACT PROCESSES IN ARMOR FABRIC PROTECTION WITH HITTING ELEMENT
(pp. 34-39)

Abstract. A solution of equationsofmotion for multilayered rectangular fabric sample when impacting by an acting object is considered. The spatial discretization by finite-element method on the basis of variational principle reduces the problem to a system of linear differential equations with variable coefficients. For integrating in time, the absolutely stable implicit scheme with a variable step is used. The multilayered sample, which is rectangular in plane, is presented in the form of a set of finite elements – parallelepipeds. The nodes of elements are located on the middle surface of a layer. A compliant base which is moved simultaneously with a bottom layer of a fabric is considered as a separate layer. Thus, each layer of the fabric is bound with a layer of net nodes that is located on the middle surface. Each element of a layer has nodescommon with next elements of the same layer and is also bound with nodes of next elements of layers adjacent with it. It determines the topology of a discrete model. Stresses and dissipative internal forces depend on desired kinematic parameters (displacements and velocities)and, as a result, the equation is non-linear. Meanwhile, the statement of effective numerical scheme for integrating the equation is expedient to carry out by approximating the solution of non-linear problem to a set of solutions of auxiliary problems that are linear within the limits of a time step. With this purpose, a discrete analog of the presented equation with unchanged time derivatives has been formed. The spectral analysis of the developed scheme shows its absolute stability. The analysis of comparing numerical calculations with experimental data shows that the obtained solution qualitatively represents the effect of “passing” the filaments by a hitting element and extending the damaged zone near the edge.

Keywords: armor fabric protection, thermomechanical processes, mathematical modeling, hitting element.

 

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