A Stiffness Surface Method to Analyze the Cross-Sectional Mechanical Properties of Reinforced Thermoplastic Pipes Subjected to Axisymmetric Loads

Axial and hoop stiffness can describe the elastic responses of reinforced thermoplastic pipes(RTPs)subjected to axisymmetric loads,such as tension,compression,pressure,and crushing loads.However,an accurate analytical prediction cannot be provided because of the anisotropy of RTP laminates.In the present study,a stiffness surface method,in which the analytical expressions of the axial and hoop stiffness are derived as two concise formulas,is proposed.The axial stiffness formula is obtained by solving the equilibrium equations of RTPs under a uniaxial stress state based on the homogenization assumption,whereas the hoop stiffness formula is derived from the combination of the elastic stability theory,the classical lamination theory,and NASA SP-8007 formula.To verify the proposed method,three types of RTPs are modeled to conduct the quasi-static analyses of the tension and crushing cases.The consistency between numerical and analytical results verifies the effectiveness of the proposed method on the prediction of the axial and hoop stiffness of RTPs,which also proves the existence of stiffness surfaces.As the axial stiffness is proportional to the radii,the axial stiffness surface consists of a series of straight lines,which can be used to predict both thin-walled and thick-walled RTPs.Meanwhile,the hoop stiffness is more applicable for thin-walled RTPs because the proposed method ignores the proportional relationship between the homogenized hoop elastic moduli and the reciprocal radii in helical structures.