Nonlinear Flexural Analysis Research Articles

Shear Failure Assessment of a G+3 RC Framed Building via Nonlinear Static Pushover Analysis using SAP2000

Accurately modelling shear behaviour in reinforced concrete (RC) structures is essential for seismic evaluation, as shear failure can lead to catastrophic outcomes. Current industry practices often emphasize nonlinear flexural analysis while underestimating the critical role of shear behaviour. This study aims to develop a nonlinear force-deformation model specifically for shear in RC sections to bridge the gap in existing literature. Standards like IS-456:2000 and ACI-318:2008 provide ultimate strength estimates but may inadequately consider the contribution of concrete under seismic loads. Insights from models by Priestley et al. (1996) and Park and Pauley (1975) are integrated to improve the calculation of shear hinge properties. A comparative nonlinear static (pushover) analysis of an RC framed building, with and without shear hinges, demonstrates the impact of shear modelling. Results show that neglecting shear hinges overestimates base shear and roof displacement capacity, masking non-ductile failure modes. Incorporating shear hinges provides a more realistic assessment of structural strength and ductility, emphasizing their necessity in seismic analysis and design. Keywords: Shear behaviour, Reinforced concrete (RC) structures, Seismic evaluation, Shear failure, Nonlinear analysis, Force-deformation model, Shear hinge.

Geometrically nonlinear large-deflection analysis of heated functionally graded composite panels with single and multiple perforations

In this article, the nonlinear flexural analysis of perforated functionally graded composite panel is performed under heat conduction and uniform/sinusoidal pressure. Here, functionally graded composite panel is modeled with single (1 × 1) and multiple (2 × 2, 3 × 3) perforations having identical surface area. A geometrically nonlinear mathematical model is adopted using the Green-Lagrange strain field via the higher-order shear-deformation mid-plane kinematics. The overall temperature-dependent elastic and thermal properties of the functionally graded (metal/ceramic) material are computed using the power-law function via Voigt’s homogenization scheme. The equilibrium equations are derived through the minimum total potential energy principle via isoparametric finite element approximations and solved further by adopting Picard successive technique. The convergence and validation of the model are carried out by performing mesh refinement and comparison tests, respectively. In adding, new numerical results for single/multiple perforated FGM panels are illustrated at various sets of parametric combinations, and compared in detail.

NURBS isogeometric-based nonlinear flexural analysis of quasi-3D surface elastic porous nanoplates

In this research work, by taking the geometrical nonlinearity together with the surface elastic-based types of size dependency, the nonlinear flexural characteristics of quasi-3D porous nanoplates in the presence and absence of a central cutout are examined via an efficient numerical strategy. Regarding to this issue, the non-uniform rational B-spline (NURBS) are put to the isogeometric methodology in order to satisfy the necessary requirements associated with the C−1-continuity. The constructed surface elastic-based plate model contains sinusoidal distribution for the shear and normal deflections by incorporating only four variables to reduce the computational cost significantly. The porosity dependency is taken into account based upon various patterns of porosity dispersion through the nanoplate thickness. The surface elastic-based nonlinear flexural responses are achieved for complete and incomplete nanoplates having central cutouts with different edge supports. It is revealed that the gap between nonlinear bending curves associated with various patterns of porosity dispersion is a bit higher for a nanoplate with lower plate thickness in which the role of surface elasticity is more significant due to a higher surface to volume ratio.

Analytical model for shear strength of prestressed hollow-core slabs reinforced with core-filling concrete

The core-filling method, one of the shear strengthening methods of prestressed hollow-core slabs (PHCSs), has been widely applied on construction sites because of its easy reinforcement procedures. However, since there are no details for sufficient composite behavior between PHCS and core-filling concrete at the inner surface of the hollow core, interfacial cracking or separation may occur when a large shear force acts on the member. Such damage at the interface can negatively affect the shear strength of the member. In this regard, this study aims to propose a shear analysis model for PHCSs with core-filling concrete that considers the composite performance between PHCS and core-filling concrete based on previous shear test results reported by the authors. In the proposed model, the shear demands of PHCS and filled cores are calculated based on nonlinear flexural analysis , and the shear force at which one of the shear demands reaches the corresponding potential strength is regarded as the shear strength of the member. In addition, the change in the shear strength of the member according to the interfacial shear properties of the PHCS and filled core is analyzed in detail. The analysis results show that the shear strength of the members is reduced as the stiffness of interfacial shear stress–slip relationship between the PHCS and filled core decreases, and that the proposed model can quantitatively estimate the shear contributions of PHCS and filled cores. • Shear resistance of hollow core slabs with core-filling concrete was investigated. • Interfacial shear stress between hollow core unit and core-filling concrete was considered. • The effect of interfacial shear on shear strength was clearly identified.

Geometrically nonlinear flexural analysis of multilayered composite plate using polynomial and non-polynomial shear deformation theories

In this paper, the geometrically nonlinear bending analysis of multilayered composite plates is carried out through a rigorous comparative study employing Green-Lagrange and von Kármán nonlinearity. The responses are analyzed for various transverse loads and boundary conditions, and emphasized the impending structural condition, which requires the consideration of full geometric nonlinearity. The study is conducted using a C0 finite element plate model using third-order and non-polynomial shear deformation theories (TSDT and NPSDT). The principle of virtual work is utilized to formulate the weak-form of governing equations, and discretized using nine-noded Lagrange elements with seven degrees-of-freedom per node. The performance of the present model has been validated by comparing present results with those available in the literature and obtained ANSYS results. The results reveal that the consideration of Green-Lagrange nonlinearity is essential for plates with all sides subjected to movable simply supported boundary conditions or with one free edge. The present study also provides a clear idea about the utilization of TSDT and NPSDT for the anti-symmetric and symmetric cross-ply plate, respectively, to get more accurate solution. Further, the effect of penalty for various theories and problems is also highlighted, and its prominent impact is asserted for some cases.

Experimental and Numerical Studies on the Structural Performance of a Double Composite Wall

In this study, experiments and numerical analyses were carried out to examine the flexural and shear performance of a double composite wall (DCW) manufactured using a precast concrete (PC) method. One flexural specimen and three shear specimens were fabricated, and the effect of the bolts used for the assembly of the PC panels on the shear strength of the DCW was investigated. The failure mode, flexural and shear behavior, and composite behavior of the PC panel and cast-in-place (CIP) concrete were analyzed in detail, and the behavioral characteristics of the DCW were clearly identified by comparing the results of tests with those obtained from a non-linear flexural analysis and finite element analysis. Based on the test and analysis results, this study proposed a practical equation for reasonably estimating the shear strength of a DCW section composed of PC, CIP concrete, and bolts utilizing the current code equations.

Nonlinear flexural analysis of composite beam with Inverted-T steel girder and UHPC slab considering partial interaction

The composite beam with inverted-T steel girder and UHPC slab connected by studs arranged in the web of the girder was developed to further the economy in material and best exploit the properties of UHPC. However, the composite beam may experience premature failure due to the occurrence of slip at the shear interface. This so-called partial interaction needs to be addressed in the flexural design for field application of the developed composite beam. The present study proposes a nonlinear analysis method for the evaluation of the flexural behavior of the composite beam considering partial interaction. An analysis method using the Fourier series to approximate the internal forces in the beam considering slip is coupled with a sectional analysis method accounting for inelastic behavior of the steel girder and nonlinear behavior of UHPC. The model considering the slip effect induced by partial interaction is seen to realistically and accurately simulate the actual behavior of the composite beam. • Shear connection with UHPC slab by studs welded on inverted-T steel girder flange. • Consideration of slip effect due to partial interaction at shear interface in analysis. • Analysis based on linear interaction theory to approximate internal forces. • Nonlinear analysis model coupling partial interaction and sectional layered analyses. • Realistic and accurate simulation of actual flexural behavior of composite beam.

Double‐mode modeling of nonlinear flexural vibration analysis for a symmetric rectangular honeycomb sandwich thin panel by the homotopy analysis method

Nonlinear flexural vibration of a symmetric rectangular honeycomb sandwich thin panel with simply supported along all four edges is studied in this paper. The nonlinear governing equations of the symmetric rectangular honeycomb sandwich panel subjected to transverse excitations are simplified to a set of two ordinary differential equations by the Galerkin method. Based on the homotopy analysis method, the average equations of the primary resonance and harmonic resonance are obtained. The influence of structural parameters, the transverse exciting force amplitude, and transverse damping to the symmetric rectangular honeycomb sandwich panel are discussed by using the analytic approximation method. Compared with the results obtained by single‐mode modeling technique, the results obtained by double‐mode modeling technique change the softening and hardening nonlinear characteristics when Ω ≈ ω1, ω1/3, and ω2/3.

Nonlinear flexural analysis of sandwich beam with multi walled carbon nanotube reinforced composite sheet under thermo-mechanical loading

AbstractNonlinear flexural analysis of sandwich composite beam with multiwall carbon nanotube (MWCNT) reinforced composite face sheet and bottom sheet under the thermo-mechanically induced loading using finite element method is carried out. Solution of current bending analysis is performed using Newton’s Raphson approach by using higher order shear deformation theory (HSDT) and non-linearity with Von Kármán kinematics. The sandwich laminated composite beam is subjected to uniform, linear and nonlinear varying temperature distribution through thickness of the beam. The sandwich beam with MWCNT reinforced composite facesheet and bottom sheet is subjected to point, uniformly distributed (UDL), hydrostatic and sinusoidal loading. The two phase matrix is utilized with E-Glass fiber to form three phase composite face sheet and bottom sheet by Halpin-Tsai model. The static bending analysis is performed for evaluating the transverse central deflection of three and five layered sandwich composite beam. Transverse central deflection is measured by varying CNT volume fraction, uniformly distributed, linearly and nonlinear varying temperature distribution, thickness ratio, boundary condition, number of walls of carbon nanotube by using interactive MATLAB code.

Flexural and Shear Performance of Prestressed Composite Slabs with Inverted Multi-Ribs

Half precast concrete slabs with inverted multi-ribs (Joint Advanced Slab, JAS), which enhance composite performance between slabs by introducing shear keys at connections between the slabs and improve structural performance by placing prestressing tendons and truss-type shear reinforcements, have recently been developed and applied in many construction fields. In this study, flexural and shear tests were performed to verify the structural performance of JAS members. Towards this end, two flexural specimens and four shear specimens were fabricated, and the presence of cast-in-place concrete and the location of the critical section were set as the main test variables. In addition, the flexural and shear performance of the JAS was quantitatively evaluated using a non-linear flexural analysis model and current structural design codes. Evaluation results confirmed that the flexural behavior of the JAS was almost similar to the behavior simulated through the non-linear flexural analysis model, and the shear performance of the JAS can also be estimated appropriately by using the shear strength equations presented in the current design codes. For the JAS with cast-in-place concrete, however, the shear strength estimation results differed significantly depending on the way that the shear contributions of the precast concrete unit and cast-in-place concrete were calculated. Based on the analysis results, this study proposed a design method that can reasonably estimate the shear strength of the composite JAS.

Design method for checking tensile stresses under service loads in cracked prestressed concrete members with 2,400‐MPa strands

SummaryThe ACI 318‐14 building code requirements specify that the net tensile stresses of prestressing strands under service loads (Δfps) shall be limited to 250 MPa for proper crack control of prestressed concrete (PC) members which are classified as Class C. However, as high‐strength prestressing strands with a tensile strength of 2,400 MPa have recently been developed and applied to PC members, this requirement needs to be reviewed. In this study, experiments and analysis were carried out in order to investigate the Δfps of PC members with the recently developed 2400 MPa strands, and in the test, the strain distributions, flexural crack widths, and stress change in bonded prestressed reinforcement were measured in detail according to the applied loads. In addition, the minimum magnitudes of effective prestress to satisfy the stress limitation of the net tensile stress of prestressing strands specified in the current design code were estimated using a nonlinear flexural analysis model, and a simplified design equation was proposed for a simple calculation of the Δfps at the design stage.

Dual potential capacity model for reinforced concrete short and deep beams subjected to shear

The dual potential capacity model (DPCM) was proposed in this study to evaluate the shear strengths of short and deep reinforced concrete (RC) members with the shear span‐to‐depth ratios less than 2.5. In the proposed model, the nonlinear flexural analysis considering the bond mechanism between steel reinforcements and surrounding concrete was conducted to estimate the local stress increase in the steel reinforcements between flexural cracks, and the shear demand force of the cracked tension zone in an RC section can also be determined on this basis. The crack concentration factor was introduced to consider the size effect in estimation of the potential shear capacity corresponding to the shear demand force to be resisted by the cracked tension zone. For the compression zone, different plasticity models were adopted depending on the shear span‐to‐depth ratio to estimate the potential shear capacity of the intact compression zone. For the verification of the proposed model, a total of 466 test results of RC short and deep beams with various shear span‐to‐depth ratios less than 2.5 were collected from existing literature, and accuracy of the proposed model was verified in detail by comparing the shear strengths of the RC short and deep test specimens estimated from the proposed DPCM with those of the test results.

Linear and nonlinear flexural analysis of higher-order shear deformation laminated plates with circular delamination

Delamination is a well-known defect mode that can arise in the manufacturing process of laminated composite plates. Due to the importance of analyzing the destructive effects of delamination on the mechanical behavior of composite plates, the flexural analysis of circular laminated composite plates with circular delamination is presented here. The governing equilibrium equations of laminated plates are first determined using third-order shear deformation theory. Both the linear and geometrically nonlinear strain states are considered, and the variational approach with a moving boundary is employed to derive the equilibrium equations. The governing equations in terms of the displacement field are then solved using the Galerkin method and the spectral homotopy analysis method to obtain the linear and nonlinear strain states, respectively. The effect of the variations of the elastic material properties on the strain energy release rate is also comprehensively studied. The results of the present study are consistent with the results of other methods found in the literature.

Large deflection model for nonlinear flexural vibration analysis of a highly flexible rotor-bearing system

Abstract Investigation of critical speeds and nonlinear free vibration analysis of a highly flexible rotor system have been studied. The rotary inertia and gyroscopic effect combined with inextensible geometric condition for pinned-guided shaft element have been taken into account to develop the governing equation of motion. The closed-form mathematical expressions have been derived for determining both linear and nonlinear natural frequencies and their behavioral patterns have been simultaneously demonstrated through time histories, FFTs and Poincare’s maps upon changing the control parameters. The nonlinear natural frequencies have been found to be higher by about 4–6% as compared to the findings obtained via linear analysis. For lower spin speed of the shaft, both linear and nonlinear forward natural frequencies have been found to be dominant. The influence of rotary inertia on natural frequencies by considering Euler and Rayleigh beam elements, separately has been reported. The system response has been observed to be either periodic or quasi-periodic depending on the spin speed. Outcomes which were not explored earlier enable significant theoretical understanding of free vibration analysis and whirling speeds of rotating system which are of great practical importance for investigating further dynamic performance.

Flexural distortional strength of steel beams determined by finite-element modelling

This paper reports on the development of a three-dimensional finite-element model for inelastic non-linear flexural buckling analysis of steel I-beams. The model was used to investigate the effects of unbraced length and yield strength on member moment capacity. Unlike existing design codes, the model considers the effect of web distortions in a lateral-distortional buckling mode. Beam slenderness ranges can be divided into three main regions depending on the failure type – low slenderness (plastic), intermediate slenderness (inelastic buckling) and high slenderness (elastic buckling). Structural design codes give criteria that specify some form of transition from the end of the elastic region to the plastic moment. In the work reported in this paper, the effect of yield strength and web distortion on the limiting laterally unbraced length for the limit state of inelastic lateral-torsional buckling (LTB) was investigated. The numerical beam strengths were compared with the design strengths predicted by current design codes, specifically the load and resistance factor design (LRFD) of the American Institute of Steel Construction (AISC), Australian Standard AS 4100 and BS EN 1993-1-2.

Nonlinear flexural analysis of single/doubly curved smart composite shell panels integrated with PFRC actuator

Abstract This article deals with the geometrical nonlinear flexural behaviour of laminated composite shell panels integrated with the piezoelectric fibre reinforced composite (PFRC) layer. In this study, the PFRC embedded panel has been modeled mathematically using Green-Lagrange nonlinear kinematics in the framework of the higher-order shear deformation theory. Moreover, the quadratic variation of the electric potential has been considered. The nonlinear finite element steps have been adopted for the discretisation of the domain. Further, the principle of minimum potential energy in conjunction with the direct iterative method is implemented to compute the desired responses. The nonlinear numerical solutions have been validated by comparing the responses with those of the available published results. The actuating capability of the present PFRC layer to suppress the linear and the nonlinear deformations of the smart composite shell panels have been investigated by using the proposed higher-order nonlinear model. Finally, the effect of different geometrical parameters (thickness ratio, aspect ratio, curvature ratio, support constraints, shell geometry and piezoelectric fibre angle) on the nonlinear static behaviour of smart composite panels has been examined by solving various numerical examples.

Nonlinear Flexural Analysis of Shallow Carbon/Epoxy Laminated Composite Curved Panels: Experimental and Numerical Investigation

AbstractIn this work, the nonlinear flexural behavior of laminated carbon/epoxy composite panels is investigated numerically using a generalized nonlinear mathematical model based on two higher-order shear deformation midplane kinematics and Green-Lagrange type geometrical nonlinearity. The exact flexural behavior of the laminated panel is computed by considering all the nonlinear higher order terms in the present mathematical model. The nonlinear governing equations are obtained using variational principles and discretized through suitable finite-element steps. The desired nonlinear responses are computed numerically using the direct iterative method. The proposed nonlinear models have been validated by comparing the responses with those available in published literature and the experiment (three-point bend test) as well. In addition, the linear and nonlinear flexural responses of the laminated carbon/epoxy flat panel are also computed using ANSYS 13.0 simulation finite element analysis package. Finally,...

Nonlinear flexural analysis of laminated composite flat panel under hygro-thermo-mechanical loading

In this article, large amplitude bending behaviour of laminated composite flat panel under combined effect of moisture, temperature and mechanical loading is investigated. The laminated composite panel model has been developed mathematically by introducing the geometrical nonlinearity in Green-Lagrange sense in the framework of higher-order shear deformation theory. The present study includes the degraded composite material properties at elevated temperature and moisture concentration. In order to achieve any general case, all the nonlinear higher order terms have been included in the present formulation and the material property variations are introduced through the micromechanical model. The nonlinear governing equation is obtained using the variational principle and discretised using finite element steps. The convergence behaviour of the present numerical model has been checked. The present proposed model has been validated by comparing the responses with those available published results. Some new numerical examples have been solved to show the effect of various parameters on the bending behaviour of laminated composite flat panel under hygro-thermo-mechanical loading.

Geometrically nonlinear flexural analysis of hygro-thermo-elastic laminated composite doubly curved shell panel

In this article, nonlinear flexural behaviour of laminated composite doubly curved shell panel is investigated under hygro-thermo-mechanical loading by considering the degraded composite material properties through a micromechanical model. The laminated panel is modelled using higher order shear deformation mid-plane kinematics and Green–Lagrange geometric nonlinear strain displacement relations. In the present case, all the nonlinear higher order terms are included in the mathematical model to obtain the exact flexure of the structural panel. The nonlinear system governing equations are derived using variational method and discretised using the nonlinear finite element steps. Numerical results are computed through direct iterative method and validated by comparing with those published results available in open literature. Finally, wide variety of numerical examples are computed using the proposed model to address the effect of hygrothermal conditions, geometrical and material parameters and support conditions on the flexural behaviour of laminated composite doubly curved shell panel.

Flexural stress analysis of uniform slender functionally graded material beams using non-linear finite element method

Functionally graded material (FGM) typically consists of two constituent materials combined together with a particular distribution. A non-linear flexural stress analysis of through-thickness functionally graded uniform slender beam, subjected to a uniformly distributed load, is studied using the versatile finite element method based on Euler–Bernoulli beam hypothesis. The von-Karman strain–displacement relations are used to account for geometric non-linearity. Simply supported and clamped FGM beams with axially immovable ends are considered. Governing non-linear equations are obtained using the principle of virtual work. Numerical results are provided to show the effect of boundary conditions and volume fraction exponent on the non-linear structural behaviour, in terms of the strains and stresses, of the FGM beams, for the first time. A shift in the neutral axis, from the mid-thickness of the beam, is observed due to the large transverse deflections, for the homogenous as well as the FGM beams. The throu...