Assessment of orthotropy assumption in (+alpha/-alpha) wrapped thick pressurized cylinders

A three-dimensional finite-element analysis was conducted to assess the accuracy of the mulitiorthotpic-layered analysis for (+o/-a ) pairs of layered thick composite cylinder subjected to internal pressure. The angle a represents the ply angle. Each ply in the F-E model was idealized by a number of 3-D anisotropic solid elements. Plane-strain and generalized plane-strain conditions were considered. The analysis was repeated for ply angles of 1,30,45,60, and 89 degrees and the number of pairs (N) ranging from 1 to 20. The mulitiorthotpic-layered analysis was conducted using the average elastic properties of +ot/-a layers. Effect of reversing the order of stacking was also analyzed. The study showed that among the six stress components the assumption of orthotropy of +a and -a pair was found to be valid for calculating the five stress components Of, OQ, az, Tzr, and tr0, provided the number of pairs is large (at least 20). The only stress that cannot be calculated from the orthotropic theory is TQZ. This stress is large (of the order of internal pressure) and it increased with increase in N. The proposed modified orthotropic analysis can be used to calculate the shear stress, IQZIntroduction Filament wound composite materials have been used in structural applications requiring high stiffness, high strength, low weight, and low cost manufacturing. Applications include submersible vessels, gun barrels, fireman gas tanks, and natural gas tanks. Design and analysis of these structures require an accurate stress analysis of layered shells, most often cylindrical shells. Monolayered anisotropic analysis of cylinders subjected to internal, external, and axial pressures were developed by Lekhnitiski [1], O'Hara [2], Shaffer[3], and Bieniek, Spillers and Freudenthal [4]. Since the filament wound composite cylinders are fabricated as a pair of + and wrap angle layers, each pair may be viewed as a single orthotropic layer. Hence the problem reduces to solution of a two-dimensional (2-D) multiorthotropic-layered shell. Stress analysis of multiorthotropic-layered cylinders with various degrees of approximations was developed by * Research Professor, Associate Fellow AIAA ** Professor, Member ASME "Copyright Q1996 by Kunigal N. Shivakumar. Published by the American Institute of Aeronautics and Astronautics, Inc.. with permission." Bieniek, Spillers and Freudenthal [4], Shaffer [5], Witherell and Scavallo [6], Roy and Tsai [7], and Witherell [8]. Among them, Roy and Tsai [7], and Witherell [8] analyses were considered to be general and accurate. Witherell's solution was an extension of Roy and Tsai [7] generalized plane-strain analysis of pressurized multiorthotropic-layered cylinders subjected to internal and external pressure. Witherell's analysis includes the effect of axial force on radial and hoop stresses and strains. Based on his analysis, Witherell developed a computer code MLCYL to analyze multiorthotropiclayered cylinders subjected to internal, external, and axial pressure with plane-strain and generalized plane-strain conditions. All these analyses are based on the homogeneous properties of +cc and -a pairs of layers (a is the fiber angle measured from the cylinder axis). Homogenization of (+oc/-a) pair decouples the normal and shear components in the elastic constitutive equation. Consequently, normal stresses induce only normal strains and the shear stresses induce only shear strains. Furthermore, no shear strains are developed due to temperature and moisture changes. Therefore, a two-dimensional orthotropic analysis is valid for homogenized +o/-a layered shells. Accuracy of this assumed orthotropy analysis, so far, has not been verified by three-dimensional (3-D) modeling of the material and analysis. The effect of warp angle (a) and number of +ot/ct pairs on the orthotropy assumption needs to be investigated. The objective of this paper was to verify the validity of homogenization of +oc /-a layers for calculating 3-D ply stresses in multilayered composite cylinders subjected to internal pressure. Then, assess the effect of warp angle (a) and number of (+oc/-a) pairs on the orthotropy assumption. Finally, develop a modified orthotropic analysis to calculate all shear stresses. A 3-D finite-element (F-E) analysis of multilayered cylindrical shell is conducted. The cylinder wall stacking sequence is represented by (+ot/-a)/v, where a is the fiber angle and N is the number of pairs. Because of more interest in thick cylinder applications, for example in cannons, a thick circular cylinder configuration is chosen. Each layer is modeled by 3-D solid anisotropic elements and stress analysis is conducted under plane-strain and generalized plane-strain conditions. Ply angles (a) considered are 1,30, 45,60, and 89 deg. Computed 3-D normal stresses are compared with orthotropic solutions [8]. Shear stresses from the modified orthotropic analysis is compared with finite-element analysis.