Thermal Stress Analysis Of Laminated Beam And Plate Structures In Temperature Environment

Composite laminated structures are widely applied in aerospace,marine engineering,civil engineering,etc.,due to their high specific strength,high specific stiffness,design flexibility,etc.However,the complex material properties of composite laminated structures make it is not accessible to predict the thermal response.In previous studies,the assumption of displacement field was introduced artificially in advance to establish the analysis model,which leads to a significant deviation between the theoretical analysis model and the actual situation.This paper establishes the analysis model through the state space method based on the three-dimensional thermoelastic constitutive equations by taking temperature,displacements,and stresses as state variables.In this process,all displacement assumptions are abandoned to ensure that the theoretical analysis model is consistent with the actual situation.In treating non-homogeneous temperature boundary conditions,the superposition principle is used to solve the temperature field step by step.The Fourier series expansion or differential quadrature method is introduced to discretize the in-plane partial differential items of state variables equivalently or discretely.According to the interlayer continuity condition of the laminated structure,the state variables of every layer are linked together by the transfer matrix method.Finally,the state variables of every layer are solved by considering the surface boundary conditions to obtain the thermoelastic solution.The main research contents of this paper are as follows:(1)The temperature field of simply supported laminated beams subjected to nonhomogeneous temperature boundary conditions is solved step by step using the superposition principle.The first part of the temperature solution satisfying the temperature boundary conditions at both ends of the laminated beam is constructed in advance.Then the general solution of temperature satisfying the second part of the temperature boundary conditions is obtained by using Fourier series expansion.The transfer matrix method is introduced to transfer the temperature and heat flux along the thickness direction of the laminated beam,and then the solution of the temperature field is solved from the surface temperature boundary conditions.The solved temperature field is considered as known loads for the laminated beam.The displacement and stress are selected as the state variables to establish the state equation based on the twodimensional thermoelastic constitutive equation.The displacement and stress of each layer are linked by the transfer matrix method.Finally,the solutions of the state variables are obtained by using the stress boundary conditions at the surface of the laminated beam.(2)For the laminated beam with clamped support at two ends and nonhomogeneous temperature boundary conditions.After the temperature field is solved by the above method,the temperature is considered as known loads for the laminated beam.The clamped boundary can be equivalent to a simply supported boundary subjected to unknown horizontal stress by introducing the unit pulse function and Dirac function.Based on the two-dimensional thermoelastic constitutive equation,the state equation is established with displacement and stress as the state variables.The state variables of every single layer are linked together by the interlayer continuity conditions through the transfer matrix method,and the state variables of each layer are determined by considering the surface stress boundary conditions.In the treatment of the clamped boundary,by fixing the finite points at the end of the beam as the equivalent effect of the clamped boundary conditions.Furthermore,the horizontal stresses at the ends of the laminated beam are solved by using the equivalent boundary conditions.Finally,the thermoelastic solution of the clamped laminated beam is obtained.(3)For laminated plates with non-homogeneous temperature boundary conditions,three different displacement boundary conditions are considered: fully clamped,fully simply supported,opposite edges simply supported and the others clamped.Based on the three-dimensional thermoelastic constitutive equation,the state equation is established with temperature,displacements,and stresses as state variables.The differential quadrature method is introduced to discretize the in-plane partial differential items of state variables.Without any additional conditions,the differential quadrature method makes the analysis model satisfy the displacement boundary conditions at the ends of the laminated plate by the state variable itself.Based on the interlayer continuity condition,the state variables are transferred along the thickness direction of the laminated plate by applying the transfer matrix method,and then the state variables of each layer are linked together.The state variables of each layer are determined by considering the stress boundary conditions at the surface of the laminated plate.Finally,the thermoelastic solution of the laminated plate is obtained.