Low Velocity Impact Analysis of Laminated Composite Plates with using modified contact law

In the present paper, a new systematic iterative analytical procedure for low-velocity impact analysis of composite plates is presented. In this method, assuming the exponential equation similar to the Hertzian contact law, using the principle of minimum potential energy and the energy-balance model between the indenter and the plate, the unknown coefficients of the exponential equation are obtained analytically. The elastic strain energy resulting from bending in the composite plate and external work due to indentation load is evaluated using an appropriate shape function for the composite plate deformation. Using the present method, in addition to reducing the runtime, the problem-solving process is carried out with appropriate convergence. Accordingly, contact coefficients for various types of composite plates with different boundary conditions have been calculated. The results are in good agreement with the experimental and numerical results. The force-time response and structure response to low-velocity impact with various boundary conditions are investigated. Also, considering the importance of physical and geometrical parameters such as mass and velocity of the impactor, the dimension of the composite plate, and the effect of these parameters on contact force history are studied. It has been shown that with increasing diameter and velocity of the impactor, exponent value in nonlinear equation contact will increase, while this parameter decreases with increasing mass of the impactor