The optimal design of the postbuckling response of variable angle tow composite structures is an important consideration for future lightweight, high-performing structures. Based on this premise, a ...new optimisation tool is presented for shell-type structures. The starting point is an isogeometric framework which uses NURBS interpolation functions to provide a smooth description of the deformed shapes, thereby reducing the number of degrees of freedom with respect to standard finite elements. The stiffness variation is obtained by exploiting the same NURBS interpolation to describe lamination parameters, employed as intermediate optimisation variables. This choice allows the design space to be thoroughly explored with relatively few design variables in a smooth optimisation space. Therefore, the optimisation strategy is divided into two stages. Firstly, the optimal distribution of lamination parameters is determined using a gradient based algorithm. Afterwards, an actual distribution of fibre orientation is retrieved. The viability of the tool is tested firstly onto a cylindrical panel under compressive loading. Then, the postbuckling optimisation of a composite wingbox is given. For both structures, the optimised postbuckling response is compared with those of the corresponding quasi-isotropic baselines showing significant improvements.
The post‐buckling strength, which is simply called as crippling, is investigated for laminated composite structures in this study. L profiles that had various stacking sequences of carbon fiber ...reinforced epoxies were tested. Three different layups configurations were used by changing flange‐to‐thickness ratios. The main objective of this research was to show that flange‐to‐thickness ratio was not the only effecting parameter for crippling. Therefore, a new parameter, EGY number, was developed by considering the positions of 0° and 45° plies. Depending on EGY number, a new semi‐empirical formulation was presented to calculate crippling strength of the laminated composite structures. One of the test results was employed to verification of EGY number. In addition, the test results were validated with finite element analyses. Static, Riks and Dynamic, Explicit computational results were compared to simulate the experiments.
Highlights
Determination of crippling strength both experimentally and theoretically.
Comparison of numerical models: Static, Riks versus Dynamic, Explicit.
Developing a new parameter called as EGY number.
Developing of a new analytical semi‐empirical formula for crippling strength.
The Effect of EGY Number on Crippling Strength for Composites
We focus on the mechanical strength of piezomagnetic beam-like nanosize sensors during post-buckling. An effective flexomagnetic property is also taken into account. The modelled sensor is selected ...to be a Euler-Bernoulli type beam. Long-range interactions between atoms result in a mathematical model based on the nonlocal strain gradient elasticity approach (NSGT). Due to possible large deformations within a post-buckling phenomenon, the resultant equations are essentially nonlinear. We establish the results using an analytical approach, including a variety of boundary conditions. We visualize the effective response of the designed sensor for several key components. It was obtained that the flexomagnetic effect is meaningful for less flexible boundary conditions. Besides, it was found that the failure originated from post-buckling occurs sooner if the numerical amounts of nonlocal parameter and the strain gradient one are respectively so small and exceedingly large.
This research employs an analytical approach to explore nonlinear torsional buckling behaviors of spiral-stiffened sigmoid FG (SSSFG) thin circular cylindrical shells. The research encompasses two ...variations of SSSFG cylindrical shells: those with internal and external spiral stiffeners. Furthermore, this study explores effects of two distinct material distributions for SSSFG cylindrical shells, specifically metal-ceramic-metal and ceramic-metal-ceramic layers, both following a sigmoid-law distribution. Theoretical formulations are obtained using the smeared stiffeners technique and classical shell theory, incorporating geometrical nonlinearity in the von-Kármán sense. The discretized nonlinear governing equations are obtained through Galerkin's method, and the approximate three-term solution for deflection is developed. Hence, explicit formulations are presented to ascertain the critical torsional load and depict the post-buckling torsional load–deflection curves. The outcomes of this study are validated by comparing them with the related research results existing in the literature. Significantly, the research highlights the influence of diverse parameters and the efficacy of stiffeners in enhancing the stability of SSSFG cylindrical shells. Researchers and engineers in this field may utilize the findings of this research as reference points for their design and research involving SSSFG cylindrical shells.
•Nonlinear torsional buckling analyses of spiral-stiffened sigmoid FG (SSSFG) thin circular cylindrical shells.•Consideration of both the shell and stiffeners as sigmoid FG materials.•Examination of two variations of SSSFG cylindrical shells: those with external and internal spiral stiffeners.•Investigation of two distinct material distributions for SSSFG cylindrical shells, specifically MCM and CMC layers.
Thin-walled composite structures operating in the post-buckling regime needs a thorough understanding of their stability behavior and failure mechanisms. For the accurate prediction of the collapse ...loads, one needs to account for the damage evolution precisely. In the current study, we have proposed a unified and generic numerical modeling approach that accounts for both the intra and inter-laminar damage modes in stiffened CFRP panels. A 3D finite element based progressive damage model (PDM) is proposed to simulate the collapse behavior of the single blade stiffened composite (SSC) CFRP panels with and without embedded de-bonding defects under uniaxial compression loading. A user-defined material subroutine based on 3D Hashin failure criteria is developed in Abaqus software to study the evolution of intra-laminar damages in SSC panel. Further, the skin-stiffener bonded interface, the inter-laminar interfaces in the skin, stiffener, including the noodle region, is modeled using the cohesive zone elements to simulate the de-bonding/delamination growth. The stability response and collapse load results obtained using the proposed PDM are compared with the experimental observations. Also, the damage evolution, failure mechanisms, the ultimate load, and the corresponding displacement data obtained from the developed PDM are validated with the experimental estimates. A comprehensive damage assessment involving the ultrasonic C-scans, infrared thermograms, and micrographic study is also carried out to supplement the PDM predictions. Thus, the proposed PDM is generic in terms of damage studies and can be used for investigating the collapse behavior of CFRP panels with multiple stiffeners.
•The attenuation of shear strain in the resin matrix near a buckled fiber was considered.•The nonlinear stress-strain relationship during the post-buckling process was investigated.•The classical ...elastic-viscoelastic correspondence principle was established to determine the dynamic buckling behaviors of SMPC at different temperatures.
The microbuckling mechanics of unidirectional fiber-reinforced shape memory polymer composite (SMPC) with low fiber volume fraction were investigated, and the mechanical models were formulated considering the attenuation of shear strain in the resin matrix near the buckled fibers. We deduced the analytical expression of the attenuation function and the key parameters during the microbuckling process of SMPC, including the critical buckling wavelength and strain. The values determined by finite element analysis verified the accuracy of the above theoretical predictions. The nonlinear stress–strain relationship during the post-buckling process was also investigated. Additionally, the classical elastic–viscoelastic correspondence principle was established to determine the dynamic buckling behaviors of SMPC at different temperatures. The viscoelastic parameters of shape memory polymer (SMP) were obtained from the isothermal stress relaxation experiments, and then the variation of buckling wavelength with time at different temperatures was evaluated.
•Using the FG-X graphene pattern in channel section struts boosts the critical buckling temperature by 12 % for clamped and 9 % for simply-supported struts, compared to the FGO pattern.•For a shape ...factor of bf/bw=0.2, changing graphene in the flanges minimally affects strut buckling temperature. However, altering the web's graphene pattern, with consistent flange reinforcement, can alter the temperature by up to 12 %.•The study on thermal pre- and post-buckling vibrations in struts with various graphene patterns reveals FGX configurations yield the highest frequencies through the pre-buckling state, though this trend shifts in the post-buckling.•Integrating an asymmetric graphene pattern (FGV) or embedding geometric imperfections sustain the primary natural frequencies of FG-GRC channel section struts above zero as they approach the critical buckling temperature.
This study explores the effect of local buckling on the compressive performance of slender structural elements, particularly those with thin-walled sections. The phenomenon of local buckling significantly reduces the axial compressive stiffness, leading to a notable decrease in the load-bearing capacity of these elements. The main goal of this research is to examine how the post-buckling characteristics of polymeric composite channel section struts can be improved under thermal loading by incorporating multi-layer graphene reinforcements. The solution methodology incorporates the von Karman geometrical nonlinearity and is based on the layerwise third-order shear deformation theory (LW-TSDT). To ascertain the precision and computational performance of the results derived from LW-TSDT, a three-dimensional (3D) finite element model is created in ABAQUS for comparative evaluation. An extensive analysis of nonlinear thermal instability in perfect and geometrically imperfect FG-GRC laminated channel section struts is undertaken to discern the graphene distribution patterns that are most and least effective in elevating the critical buckling temperature and natural frequencies through pre- and post-buckling conditions. The comparative analysis indicates that employing the FG-X graphene distribution pattern across the thickness of the web and flanges in channel section struts leads to a projected increase of 12 % in the critical buckling temperature for clamped channel section struts, in contrast to those that adopt the FGO graphene distribution pattern. For cases with simply-supported boundary conditions, this increase is noted to be approximately 9 %. Moreover, findings confirm that incorporating an asymmetric graphene distribution pattern (FGV) or introducing geometrical imperfections in the flanges and web that generate a bending moment within the structure from the beginning of thermal loading effectively prevents the primary natural frequencies of FG-GRC channel section struts from declining to zero close to the critical buckling temperature. This is significantly different from scenarios involving perfectly structured and symmetrically reinforced graphene distribution patterns such as FGX.
Elastic ribbons possess the capacity to undergo stretching, bending, and twisting, resulting in a diverse range of morphologies. In this study, we conduct both experimental and numerical ...investigations into the torsional instabilities of clamped ribbons subjected to stretching and twisting loads. The extended Föppl-von Kármán plate model is employed to describe the torsional and tensile responses prior to buckling. Through finite element simulations, we accurately capture the observed evolution of morphologies, spanning from the initial helicoid to a double-layer helicoid, and ultimately to a scrolled yarn structure. As the formation of the double-layer helicoid, the torque, which decreases with the twist during the transverse bending and folding process, gradually increases with the twist until the occurrence of a secondary instability. Furthermore, initial pre-tension enhances the ribbon's capacity to endure torsional deformation, leading to corresponding increases in torque and tension. These findings hold implications for comprehending the intricate deformation mechanisms of slender structures.
•The experimental morphological transitions of a twisted ribbon, from helicoid to double-layer helicoid, and finally to a yarn configuration, are captured through FE simulation.•The formation of the double-layer helicoid in the ribbon enables it to withstand transverse bending once more until the occurrence of secondary instability.•Pre-tension enhances the ribbon's capacity to endure torsional deformation, resulting in corresponding increases in torque and tension.
This is a fundamental study on the buckling temperature and post-buckling analysis of functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) disk covered with a piezoelectric ...actuator and surrounded by the nonlinear elastic foundation. The matrix material is reinforced with graphene nanoplatelets (GPLs) at the nanoscale. The displacement–strain of thermal post-buckling of the FG-GPLRC disk via third-order shear deformation theory and using Von Karman nonlinear plate theory is obtained. The equations of the model are derived from Hamilton’s principle and solved by the generalized differential quadrature method. The direct iterative approach is presented for solving the set of equations that includes highly nonlinear parameters. Finally, the results show that the radius ratio of outer to the inner (
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), the geometrical parameter of GPLs, nonlinear elastic foundation, externally applied voltage, and piezoelectric thickness play an essential impact on the thermal post-buckling response of the piezoelectrically FG-GPLRC disk surrounded by the nonlinear elastic foundation. Another important consequence is that, when the effect of the elastic foundation is considered, there is a sinusoidal effect from the
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parameter on the thermal post-buckling of the disk and this matter is true for both boundary conditions.
In this study, the unified formulation of a full geometrically nonlinear refined plate theory in a total Lagrangian approach is developed to study the post-buckling and large-deflection analysis of ...sandwich functionally graded (FG) plate with FG porous (FGP) core. The plate has three layers so that the upper and lower layers are FG and the middle layer (core) is the FGP, which is considered with four cases in terms of the porosity core distribution. The different two-dimensional (2D) plate structures kinematics are consistently implemented based on the Carrera’s Unified Formulation (CUF) by means of an index notation and an arbitrary expansion function of the generalized variables in the thickness direction, leading to lower- to higher-order plate models with only pure displacement variables. Furthermore, a finite element approximation and the principle of virtual work are used to easily and straightforwardly formulate the nonlinear governing equations in a total Lagrangian manner, whereas a path-following Newton-Raphson linearization scheme based on the arc-length constraint is utilized to solve the full geometrically nonlinear problem. Numerical assessments are finally conducted to confirm the capabilities of the proposed CUF plate model to predict the post-buckling and large-deflection equilibrium curves with high accuracy.
