Deokjoo Kim

Full and von Karman geometrically nonlinear analyses of laminated cylindrical panels

A total Lagrangian-type nonlinear analysis for prediction of large deformation behavior of thick laminated composite cylindrical shells and panels is presented. The analysis, based on the hypothesis of layerwise linear displacement distribution through thickness, accounts for fully nonlinear kinematic relations, in contrast to the commonly used von Karman nonlinear strain approximation, so that stable equilibrium paths in the advanced nonlinear regime can be accurately predicted. The resulting degenerated surface-parallel quadratic (16-node) layer element, with 8 nodes on each of the top and bottom surfaces of each layer, has been implemented in conjunction with full and reduced numerical integration schemes to efficiently model both thin and thick shell behavior. The modified Newton-Raphson iterative scheme with Aitken acceleration factors is used to obtain hitherto unavailable numerical results corresponding to fully nonlinear behavior of the analyzed panels. A two-layer [0/90] thin/shallow clamped cylindrical panel is investigated to assess the convergence rate for full and reduced integration schemes and to check the accuracy of the present degenerate cylindrical shell layer element. Accuracy of the von Karman nonlinear approximation, currently employed in many investigations on buckling/postbuckling behavior of thin shells, is assessed, in the case of laminated thin cylindrical panels, by comparing the numerical results obtained using this approximation with those due to fully nonlinear kinematic relations, especially in the advanced stable postbuckling regime.

On propagation of shear crippling (kinkband) instability in a long imperfect laminated composite cylindrical shell under external pressure

Abstract A fully nonlinear analysis for prediction of shear crippling (kinkband) type propagating instability in long thick laminated composite cylindrical shells is presented. The primary accomplishment of the present investigation is prediction of equilibrium paths, which are often unstable, in the presence of interlaminar shear deformation, and which usually deviate from the classical lamination theory (CLT)-based equilibrium paths, representing global or structural level stability. A nonlinear finite element methodology, based on a three-dimensional hypothesis, known as layerwise linear displacement distribution theory (LLDT) and the total Lagrangian formulation, is developed to predict the aforementioned instability behavior of long laminated thick cylindrical shell type structures and evaluate failure modes when radial/hydrostatic compressive loads are applied. The most important computational feature is the successful implementation of an incremental displacement control scheme beyond the limit point to compute the unstable postbuckling path. A long (plane strain) thick laminated composite [90/0/90] imperfect cylinder is investigated with the objective of analytically studying its premature compressive failure behavior. Thickness effect (i.e. interlaminar shear/normal deformation) is clearly responsible for causing the appearance of limit point on the postbuckling equilibrium path, thus lowering the load carrying capability of the long composite cylinder, and localizing the failure pattern, which is associated with spontaneous breaking of the periodicity of classical or modal buckling patterns. In analogy to the phase transition phenomena, Maxwell construction is employed to (a) correct the unphysical negative slope of the computed equilibrium paths encountered in the case of thicker cylinders modeled by the finite elements methods that fall to include micro-structural defects, such as fiber waviness or misalignments, and (b) to compute the propagating pressure responsible for interlaminar shear crippling or kinkband type propagating instability. This type of instability triggered by the combined effect of interlaminar shear/normal deformation and geometric imperfections, such as fiber misalignment, appears to be one of the dominant compressive failure modes for moderately thick and thick cylinders with radiusto-thickness ratio below the corresponding critical value. A three-dimensional theory, such as the LLDT, is essential for capturing the interlaminar shear crippling type propagating instability.

Localization and shear-crippling (kinkband) instability in a thick imperfect laminated composite ring under hydrostatic pressure

Abstract A fully nonlinear finite elements analysis for prediction of localization representing shear-crippling (kinkband) instability in a thick laminated composite (plane strain) ring (infinitely long cylindrical shell) under applied hydrostatic pressure is presented. The primary accomplishment of the present investigation is prediction of meso(lamina)-structure-related equilibrium paths, which are often unstable in the presence of local imperfections and/or material nonlinearity, and which are considered to “bifurcate” from the primary equilibrium paths, representing periodic buckling patterns pertaining to global or structural level stability of the thick cross-ply ring with modal or harmonic imperfection. The present nonlinear finite elements solution methodology, based on the total Lagrangian formulation, employs a quasi-three-dimensional hypothesis, known as layerwise linear displacement distribution theory (LLDT) to capture the three-dimensional interlaminar (especially, shear) deformation behavior, associated with the localized interlaminar shear-crippling failure. A thick laminated composite [90/0/90] imperfect (plane strain) ring is investigated with the objective of analytically studying its premature compressive failure behavior. Numerical results suggest that interlaminar shear/normal deformation (especially, the former) is primarily responsible for the appearance of a limit (maximum pressure) point on the post-buckling equilibrium path associated with a periodic (modal or harmonic) buckling pattern, for which a modal imperfection serves as a perturbation. Localization of the buckling pattern results from “bifurcation” at or near this limit point, and can be viewed as a symmetry breaking phenomenon. In order to investigate a localization of the buckling pattern, a local or dimple shaped imperfection superimposed on a fixed modal one is selected. With the increase of local imperfection amplitude, the limit load (hydrostatic pressure) decreases, and also the limit point appears at an increased normalized deflection. Additionally, the load–deflection curves tend to flatten (near-zero slope) to an undetermined lowest pressure level, signaling the onset of “phase transition” in the localized region, and coexistence of two “phases”, i.e., a highly localized band of shear crippled (kinked) phase and its unshear-crippled (unkinked) counterpart along the circumference of the ring. Interlaminar shear-crippling triggered by the combined effect of imperfection, material nonlinearity and interlaminar shear/normal deformation appears to be the dominant compressive failure mode. A three-dimensional or quasi-three-dimensional theory, such as the afore-mentioned LLDT is essential in order to capture the meso-structure-related instability failure such as localization of the interlaminar shear crippling, triggered by the combined presence of local imperfection and material nonlinearity.