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3h approaches infinity 3h equal absorption of electromagnetic back surfaces Bernoulli numbers biharmonic functions bj are obtained bQ and bj constant heat constant internal heat deformation parameter cp differential operation intended dimensionless Effect of ph electromagnetic radiation equa equation 29 equation 40 equations 12 Equations 37 Equations governing Euler numbers function an(x,y functions T0 in-plane incident energy distribution internal heating function Langley Research Center large surfaces linear absorption coefficient magnitude midplane obtained from equations P0 and bj plate and shell plate material plate temperature parameters plate thermal-deformation parameters plate thickness Poisson's equation power series recurrence relation reference 14 relationships between T0 resulting expressions set of equations small-deflection plate deformations specified temperature boundary steady-state temperature distribution substituting equation T0 and P0 temperature boundary conditions temperature gradient terms of bQ terms of T0 thermal conductivity Thermal Stresses tion unaffected by heat value of 3h zero zn+2