Nonlinear Deflection Response Research Articles

Computational modelling and prediction of nonlinear deflection responses of bonded joint component with multiple damage (crack and delamination) – An experimental validation

The present research evaluates the presence of damage, including delamination and cracks, affects the deflection response of an adhesively bonded single lap joint (SLJ). In this study, the numerical analysis is performed for intact and influence of different damages in the adherend of SLJ in the commercial simulation software (ABAQUS). The circular delamination of radius ‘R’ 10 mm and crack having length ‘l’ 20 mm, the radius of curvature ‘Rc’ 0.2 mm are imposed into the laminate adherend using node-to-surface interaction technique. The stability of the simulation model is verified by comparing the deflection values from published results and experimental data. The confirmed simulation model is broadened to examine the impact of design factors (fiber orientation, loading position, delamination shape, crack position and orientation, and delamination position with and without crack) on the deflection response for various overlapping lengths (25, 30, 35, and 40 mm) for final design recommendation. Additionally, the sensitivity analysis was performed using a surrogate model (i.e., variance-based method) by constructing the second-order polynomial function to quantify the influence of damages under the input parameters. The detailed features and multivariate model functions have been analysed for the various damage cases of SLJ.

Nonlinear Deflection Characteristics of Weakly Bonded Curved Composite Structure Under Hygro-Thermo-Mechanical Loadings

A customized MATLAB algorithm is developed for internally separated laminated composite panels experiencing large geometric deformations. The algorithm is designed to calculate nonlinear deflection responses under the effect of combined hygro-thermo-mechanical (HTM) loading. The hygrothermal (HT) load on the panel is in-plane, whereas the mechanical load acts upon the structure transversely. The analysis has adopted various kinematic theories and finite element (FE) techniques to determine the deformations computationally. The deflection behavior of the composite is characterized through a macro mechanical model considering the nonlinearity in geometry with and without accounting for the stretching effects across the panel thickness. Additionally, the changes in composite properties due to the environment and/or loadings are adopted to achieve a realistic response, preserving continuity assumptions between the individual layers of the weakly bonded structure. Moreover, various numerical examples are examined through different models to illustrate the influences of environmental factors and design-specific parameters on the flexural strength of weakly bonded structures. The findings strongly emphasize the necessity of employing diverse kinematic models when examining laminated structures, both with and without HT loading, while also acknowledging the potential for debonding.

Nonlinear deflection characteristics of damaged composite structure theoretical prediction and experimental verification

This research derived a nonlinear computational model for the prediction of deflection responses of the damaged layered composite structures. The model validity was verified using in-house experimentation. The composite panel model has been derived mathematically using the higher-order polynomial kinematics without non-zero shear stress conditions and Green’s strain for the geometrical nonlinearity. The nonlinear deflection responses of combined damage curved shell structures are evaluated numerically utilizing the nonlinear isoparametric finite element technique in conjunction with the direct iterative method. By setting the necessary convergence criteria, the model accuracy has been explored by comparing the deflections of the published literature (the maximum deviation observed is 6.97%). Additionally, the experimentation is done on damaged laminated shell structures, and results are compared to show the proposed model’s efficacy (maximum deviation observed is 2.17%). Finally, a number of numerical examples are solved to assess the effects of the material, geometry and damage-related parameters on the nonlinear deflections of the shell structure.

Nonlinear static and dynamic (deflection/stress) responses of porous functionally graded shell panel and experimental validation

The static and dynamic characteristics of functionally graded (FG) structures have been investigated in this article, considering full geometrical nonlinearity. The finite element (FE) solutions are obtained for the graded panel by modelling through higher-order kinematics (HSDT) and Green-Lagrange strain-displacement relations (GLNST). The desired graded panel properties are obtained through Voigt’s micromechanical approach, considering different grading patterns (exponential, EPL; sigmoid, SGM and power law, POL). Additionally, to maintain the generality of the graded structure, different porosity distribution types (even and uneven, EVP and UEP) are incorporated into the proposed mathematical model. Further, the numerical solutions are obtained using Newmark’s method’s direct iterative technique and constant integration steps. The solution sensitivities are verified for the developed algorithm via adequate convergence and comparison tests. In addition, the experimental validation is performed using the layerwise fabricated luffa-fibre reinforced FG plates to validate the proposed theoretical model’s accuracy. Lastly, the responses are computed using the newly derived model for the variable design-dependent parameters associated with the FG structural geometry and properties. The final deliverables, that is the nonlinear deflection responses (NDFR)/stress values, are discussed under mechanical loadings (static and dynamic).

Investigation on nonlinear bending behavior of sandwich shell panel with cutout using HSDT and FE approach

The nonlinear deflection response of the sandwich shell panel with cutout is analyzed, numerically in the present article. The numerical model of the said curved panel is derived using higher-order shear deformation theory and finite element approximations. The geometrical nonlinearity is being considered via Green-Lagrange’s strain-displacement relation. The governing equation of the nonlinear bending analysis is derived using the energy approach and variational principle. Model accuracy is analyzed as a first step by matching current model responses with previously available data. Further, the model’s capability is explored by solving various new numerical examples and discussed in detail.

Testing and modeling of deep beams strengthened with NSM-CFRP reinforcement around cutouts

The behavior of reinforced concrete (RC) deep beams strengthened with near-surface-mounted carbon fiber-reinforced polymer (NSM-CFRP) reinforcement around cutouts is examined in this study. The study comprised experimental testing, numerical simulation, and strut-and-tie modeling (STM). Three different NSM-CFRP strengthening solutions around the cutouts were developed using STM. The investigated parameters included the amount and orientation of NSM-CFRP reinforcement. The NSM-CFRP solutions fully restored the original shear strength, except in two cases where only 93 % and 94 % of the capacity were restored. Finite element (FE) models were developed to simulate the nonlinear behavior of the tested beams. The strength predicted by the FE models were insignificantly different from those measured experimentally. The nonlinear deflection response, CFRP strain response, and crack patterns predicted numerically were in good agreement with those obtained from the tests. The STM tended to provide a conservative prediction for the nominal strength of the tested beams.

Influence of debonding on nonlinear deflection responses of curved composite panel structure under hygro-thermo-mechanical loading–macro-mechanical FE approach

The excess geometrical deformation due to the in-plane hygrothermal and transverse mechanical loading are computationally (through a customized MATLAB code) obtained for the weakly bonded structure using the different kinematic theories in combination with the finite element steps. To evaluate the nonlinear deflection data a macro mechanical model is prepared mathematically considering the stretching effect (through the thickness), as well as the constant functions of displacement. The model includes the variation of composite properties due to the change in environmental temperature and moisture content including the necessary continuity assumptions between the separated layers for the weak bonding. The role of delamination i.e. location, position and size on the nonlinear deflection parameters are also computed under the combined loading (Hygral/Thermal/Mechanical/Hygro-Thermo-Mechanical). The solution accuracy and the elemental sensitivity have been computed for the proposed macro mechanical finite element model. Moreover, a set of numerical examples are solved to show the environmental effect on the flexural strength of a weakly bonded composite panel including the design-dependent parameters. The final results are indicating the necessity of the various kinematic model for the analysis of laminated structure with/without hygrothermal loading as well as the debonding.

Large deflection response-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes

This paper deals with the nonlinear large deflection analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates and panels using a finite element method. Based on the first-order shear deformation theory (FSDT), the proposed model takes into account the transverse shear deformations and incorporates the geometrical nonlinearity type. A C0 isoparametric finite shell element is developed for the present nonlinear model with the description of large displacements and finite rotations. By adopting the extended rule of mixture, the effective material properties of FG-CNTRCs are approximated with the introduction of some efficiency parameters. Four carbon nanotube (CNT) distributions, labeled uniformly distributed (UD)-CNT, FG-V-CNT, FG-O-CNT, and FG-X-CNT, are considered. The solution procedure is carried out via the Newton-Raphson incremental technique. Various numerical applications in both isotropic and CNTRC composite cases are performed to trace the potential of the present model. The effects of the CNT distributions, their volume fractions, and the geometrical characteristics on the nonlinear deflection responses of FG-CNTRC structures are highlighted via a detailed parametric study.

The nonlinear deflection response of CNT/nanoclay reinforced polymer hybrid composite plate under different loading conditions

The carbon nanotubes (CNTs) are used as significant reinforcement materials in the advanced composites due to their improved mechanical properties. The carbon nanotubes reinforced nanocomposites have improved mechanical strength, and stiffness properties in addition to their reduced weight. Only a few percentages of CNTs (2–5% by weight) could be added to these nanocomposites as more volume fraction will deteriorate their mechanical properties. A computational approach is used in the present investigation to find the mechanical properties of the hybrid nanocomposite which is modeled by adding nanoclay particles into the conventional CNTs reinforced epoxy system. Using Halpin-Tsai approach (which is based on the micromechanical modeling) the mechanical properties of hybrid nanocomposites are evaluated. The effect of the CNTs and the nanoclay particles on the nonlinear transverse central deflection response of nanocomposite plate under different loading conditions is studied in detail. The simulation results of present investigation have been validated with the data sets of the deflection responses available in the references.

Numerical investigation on the nonlinear flexural behaviour of wrapped glass/epoxy laminated composite panel and experimental validation

In this work, the geometrically nonlinear deflection responses of glass/epoxy composite flat/curved shell panel structure have been analysed theoretically with the help of three different displacement field kinematics and Green–Lagrange strain–displacement relation. In this analysis, the numerical models are developed based on two higher-order shear deformation mid-plane kinematics and one simulation model with the help of commercial finite element package (ANSYS). The present mathematical model is general in the sense that it includes all the nonlinear higher-order terms arising due to Green–Lagrange strain–displacement relation to capture the exact flexural strength of the laminated structure. The present nonlinear model is so generic that it can be easily extended for solving different kinds of geometrical configurations (spherical, cylindrical, elliptical, hyperboloid and plate). The equilibrium equation of the transversely loaded panel is achieved by minimizing total potential energy expression and discretized using the suitable finite element steps. The required deflection values are computed numerically via a homemade MATLAB code in conjunction with Picard’s iterative method. Consequently, the stability of the present numerical solutions has been established through the convergence test and validated by comparing the results with those available published results. In addition, the transverse deflections are obtained experimentally via three-point bend test and utilized for the comparison purpose to demonstrate the significance of the newly developed higher-order finite element model.

Geometrically nonlinear isogeometric analysis of functionally graded plates based on first-order shear deformation theory considering physical neutral surface

This paper presents the geometrically nonlinear isogeometric analysis of functionally graded material (FGM) plates based on the first-order shear deformation theory considering the physical neutral surface. According to the power law distribution of volume fraction of constituents, the material properties of plate are assumed to vary through the thickness. The transverse shear correction factor is evaluated through the energy equivalence and the geometric nonlinearity is accounted for von Kármán strain for dealing with small strain and moderate rotation. The quadratic NURBS (Non-Uniform Rational B-Spline) elements are used to construct physical meshes in C1 continuity which is required for the generalized displacements. A numerical analysis is performed on the examples of square plates with various boundary conditions and clamped circular plate. The obtained results are compared with the previously published results in order to show the accuracy and effectiveness of present approach. The effects of shear correction factors, gradient index and different boundary conditions on the geometrically nonlinear deflection response of FGM plates are parametrically investigated.

Strength of Composite T-Joints under Pull-Out Loads

This paper examines the non-linear deflection response of highly stressed sandwich T-joints using large deflection and plasticity analyses. The finite element method considering a plane model of the joint, accounts for plastic deformation of the core and glue materials and non-linear geometric effects. The finite element studies are used to identify internal stress states in the various regions of the joint and for different attachment configurations, leading up to and at failure. The results of this analysis have been combined with the measured properties of the materials forming the joint in order to predict quantitatively the failure strength.

The non-linear response of transversely-loaded folded plate structures

The folded-plate or “prismatic shell” structure has often provided in the past an economical solution to the problem of roofing large clear areas in a wide variety of building types including hangars for aircraft, auditoriums, gymnasiums, factories, supermarkets and similar major structures. Previous attempts to solve the stress analysis problem for this type of structure employed certain approximations or “linearizations”, which have proven to be satisfactory for the purpose of predicting stresses but not entirely satisfactory for the purpose of predicting deflections. Test results from ten aluminum model specimens, which indicate that deflections occurring in folded plate structures in response to the application of transverse loads are non-linear, are summarized herein. In addition, a new analytical approach based on the principle of minimum potential energy and utilizing the Rayleigh-Ritz method is proposed herein which specifically treats the described non-linear deflection response problem.