Semi-analytical solution of three-dimensional thermoviscoelastic behaviors for a fiber metal laminated plate subjected to laser shock processing

Abstract The three-dimensional transient temperature distribution for a fiber metal laminated (FML) rectangular plate during laser shock processing has been obtained previously based on the separate variable method (SVM). Then the three-dimensional thermoviscoelastic governing equations are formulated based on Hamilton variational principle subsequently. The obtained thermoviscoelastic nonlinear integral-partial differential equations are solved by applying the Galerkin method and Newmark method in space and time domain, respectively, which differs with other publications. Meanwhile, Newton-Cotes trapezoidal formula is adopted to conduct the convolution operator for the transforming algebraic equations. The research aims at giving the semi-analytical solution of three-dimensional thermoviscoelastic behaviors for the FML structure subjected to laser shock processing, besides understanding the influences of temperature, boundary condition, laser moving velocity as well as number of fiber species and FML layers on the dynamic characteristic (such as deflection, vibration frequency and stress components) of the FML structure. Comparing with the deflection, the in-plane displacement is more sensitive to the temperature parameter, and normal stress caused by temperature is far greater than that caused by deformation. Young's modulus E2 for S2-glass fiber epoxy is less than that of glass polymer about 61.7%; shear stress σxy is only associated with shear modulus G x y l ( t ) ; Shear stress σxz is only associated with rotation angle φ and deflection, while normal stress is associated with in-plane displacement and temperature increment.