In-plane Loading Research Articles

Static stability of functionally graded porous nanoplates under uniform and non-uniform in-plane loads and various boundary conditions based on the nonlocal strain gradient theory

This work examines the buckling behavior of functionally graded porous nanoplates embedded in elastic media. Size effects are added to the nanoplate constitutive equations using nonlocal strain gradient theory. The four-variable refined plate theory is employed for nanoplate modeling. This theory assures stress-free conditions on both sides of the nanoplate and has less uncertainty than high-order shear deformation theories. It is postulated that the nanoplate experiences in-plane compressive loads, which may have both linear and nonlinear distributions. Additionally, uniform and non-uniform porosity distributions are considered. The governing partial differential equations are extracted using the notion of the minimal total potential energy. Following this, the Galerkin method is employed to solve these equations utilizing trigonometric shape functions. Simple, clamped, and combined boundary conditions for nanoplate edges are studied. Once the governing algebraic equations were extracted, the critical buckling load of the nanoplate is determined. To conduct a validation study, the obtained data are juxtaposed with the findings of previous studies, revealing a notable level of concurrence. After the critical buckling load has been ascertained, an inquiry is undertaken to assess the influence of various parameters including nonlocal and length scale parameters, boundary conditions, porosity distribution type, in-plane loading type, geometric dimensions of the nanoplate, and stiffness of the elastic environment, on the static stability of nanoplates.

Modified Study for the Effect of Combined Cycling Loading in Plane on Dynamic Edge Crack Propagation in a Thin Plate

نظرا للأهمية والمخاطر المحتملة المرتبطة بحدوث الشقوق الميكانيكية في التطبيقات الهندسية الهامة، فقد أصبح من الضروري البحث عن نوع معين من انتشار الشقوق. هذه هي حالة شقوق الوضع المختلط التي تنتج عن الوضع الأول والوضع الثاني للتحميل والتي تنتشر في معظم الهياكل، ويتم عرض تلك الشقوق، بالإضافة إلى الظروف التي يمكن أن تحدث فيها، في هذه الحالة. في سياق نظرية ميكانيكا الكسر المرنة الخطية (LEFM)، تم تحقيق توليد إمكانية التحميل غير المتناسب على عينات من سبائك الألومنيوم من خلال تطبيق أحمال الشد الثابتة بالتزامن مع أحمال القص الدورية. باستخدام قانون جريفيث للوضع المختلط I/II لطاقة الشق، تم بناء معادلة نظرية لمعدل نمو الشق الديناميكي. تأخذ هذه المعادلة في الاعتبار تأثير انتشار الكراك الديناميكي. تجريبياً تم تصميم أجهزة مختبرية محلية الصنع وتعديلها لتتناسب مع طبيعة الأحمال المطبقة على عينات ذات شقوق حافة مسبقة من نوعين مختلفين من سبائك الألومنيوم (AA) 6061 و5052، بنظام Uni-Standard بطول شق الحافة تم إجراء مقارنة بين أنواع السبائك المستخدمة للتحقق من صحة النتائج. والتناقض بين مدى قرب النتائج النظرية من النتائج الحقيقية للكسر الذي حدث. وأظهرت النتائج التوافق بين المعادلة النظرية والنتائج العملية. تبدأ العينة 5052 بشكل أسرع وتنتشر الشقوق بشكل أسرع من السبائك 6061.

Experimental and numerical investigations on the impact of openings on the stiffness of CLT shear walls

Cross-laminated timber (CLT) exhibits high in-plane strength and stiffness, positioning it as a viable material for shear walls in seismic regions. However, the influence of openings on the in-plane stiffness of CLT shear walls remains inadequately studied. In this study, 43 CLT shear walls with different opening sizes were tested under in-plane loading. The stiffness reduction was less than 29% for openings 800×800mm (53% of panel width), but exceeded 60% for openings 1200×1200mm (80% of panel width). When assessed with identical opening sizes, 139mm and 175mm thick CLT shear walls displayed consistent stiffness reductions. Panels with an aspect ratio of 3:1 exhibited a more pronounced drop than 2:1 aspect ratio panels. A validated 3D finite element model was used to investigate the influence of panel layup and opening shape and location on the in-plane stiffness reduction. For a distance between the opening and panel edge exceeding 300mm, the shape and location of openings exerted negligible effects. Finally, the Dujič’s model was shown to be a suitable predictor to evaluate the in-plane stiffness reduction of CLT shear walls with openings.

A super element model for failure analysis of masonry buildings under lateral in-plane loading

This study developed a discrete element-based approach called Super Element Model to estimate the non-linear behavior and damage propagation of multi-story and multi-span masonry buildings subjected to in-plane lateral loads. To this aim, the piers and spandrels were substituted by a super element constituted by four large isosceles triangular panels and eight connector links, while the cross-joint areas remained rectangular. Two vertical/horizontal links also represent the connection of the super element of piers/spandrels to the cross-joint panels at each end. The large panels were assumed to behave elastically and inelasticity was only concentrated at the connector links. All the connector links were bi-component springs considering axial and shear behavior. With the help of masonry stress–strain curve, a simplified bi-linear behavior was extracted for springs. Thanks to the appropriate geometrical configuration of the piers’ equivalent super element, a dynamic interaction was provided between lateral capacity and normal stresses originating from lateral loads. After presenting a step-by-step algorithm for the model implementation in commercial software, two full-scale masonry buildings were chosen for validation purposes. The obtained results proved the proposed Super Element Model is reliable and user-friendly.

Horizontal mechanical performance of the upper beam frame with beam-beam connection of traditional wooden building

This paper presents the analytical model of the beam-beam connection (BBC) and studies the horizontal mechanical performance of the upper beam frame assembled by BBC. The different compressive stress distributions at the contact interfaces of the BBC with intersection angles 2π/4, 2π/5, 2π/6, 2π/7 and 2π/8 are analyzed when it rotates in clockwise and anticlockwise directions, also the deformation and friction characteristics of the BBC with intersection angles 2π/5, 2π/6, 2π/7 and 2π/8 when it rotates in two directions are discussed, then the analytical model of the BBC is proposed. Also, the moment-angle curves of the proposed model with multiple angles are checked by the results of the numerical models in Abaqus. Furthermore, the horizontal mechanical performance of the upper beam frame assembled by BBC is studied under in-plane load. The results show that frictional slip at the contact interfaces of BBC with angles 2π/5, 2π/6, 2π/7 and 2π/8 when it rotates in anticlockwise direction should be considered in modeling process, and it can be ignored of BBC with angles 2π/4, 2π/5, 2π/6, 2π/7 and 2π/8 when it rotates in clockwise direction. The results of the proposed model agree with those of the numerical model basically. The resistance increases with the number of the beams of frames, and the resistance characteristics of the hexagonal and octagonal frames are similar. The research results can be further applied to the model analysis of beam-column structures of the traditional Chinese wooden building.

Nonlinear thermal flutter of variable angle tow curved panels with elastically restrained edges in supersonic airflow by generalized Galerkin method

Variable Angle Tows (VAT) composite materials can effectively transfer major stresses from the interior region to the edges through in-plane load redistribution, thereby significantly enhancing their structural performance. Therefore, correct handling of boundary conditions is crucial in analyzing VAT structures. Considering that most practical engineering cases involve non-ideal or non-classical boundary support, this paper proposes an efficient method to address the nonlinear thermal flutter problem of elastic supported VAT curved panels in supersonic airflow. Assuming the fiber orientation angle varies in four different ways along the x-direction, the basic equations are established based on the von Kármán large deformation plate theory and the first-order piston theory. The generalized Galerkin method, capable of handling arbitrary elastic boundary constraints, is used to solve the problem in the space domain, while the Runge-Kutta method is applied in the time domain. Numerical examples illustrate how elastically restrained conditions, fiber orientation angles, height-rise ratio, and thermal loads, along with aerodynamic pressure, influence flutter responses of VAT panels. The presented method can be used for the aeroelastic stability design of VAT curved panels under arbitrary boundary conditions.

The interaction between a piezoelectric screw dislocation and collinear rigid lines in one-dimensional hexagonal quasicrystals

The interaction between a piezoelectric screw dislocation and collinear rigid lines in one-dimensional (1D) hexagonal quasicrystals (QCs) under anti-plane mechanical and in-plane electrical loading is analysed. Two idealized electrical assumptions, namely electrically conductive and dielectric, are considered. By using Muskhelishvilid’s complex transformation method, the explicit expressions for the field variables, the singularity of the field variables at the line tip and the force on the dislocation are obtained for a single rigid line. Based on the generalized Peach–Koehler formula, the generalized stress intensity factors and image force on dislocations in piezoelectric quasicrystal (PQC) are obtained. It is evident that the existence of phason field has an effect on image force.

Local-global buckling interaction in steel I-beams—A European design proposal for the case of fire

This paper presents a comprehensive review of the developments leading to the proposal of European fire design rules for steel beams with thin-walled I-sections. Thin-walled beams are favoured in steel construction due to their structural efficiency, however they are prone to buckle when subjected to in-plane loads, phenomenon which requires a thorough investigation. The focus lies on addressing the interaction between local and global buckling in these members. This study discusses modifications to the Effective Width Method at elevated temperatures, aiming to rectify underestimation of section capacity on certain cross-sections. Additionally, an overview of lateral-torsional buckling resistance is provided, being a new Effective Section Factor proposed to account for its interaction with local buckling. The paper revisits the European fire design proposal, comparing the improvements of the existing Eurocode 3 Part 1–2 (EN1993-1-2:2005) relative to the recent second generation of Part 1–2 of Eurocode 3 (FprEN1993-1-2:2023) through an extensive numerical study. Limitations and future research directions are also discussed, such as dependency on the section classification and broadening the application scope of these rules to higher steel grades.

Research on the influence of out-of-plane loads on the fatigue life of metal structures

Abstract For civil aircraft structures, in-plane tensile, compressive, shear, and their combined forms of loads are the usual loads on plate and shell structures, while bending moments, torsion, and other forms of loads are mainly borne by assemblies consisting of multiple parts. However, some plate and shell structures are subjected to in-plane loads while also being affected by out-of-plane loads. In order to study the difference between the fatigue performance of plate and shell structures under the influence of out-of-plane load and the fatigue performance under the effect of pure in-plane load, the axial tensile fatigue test considering the out-of-plane load is carried out, which demonstrates the negative effect of the out-of-plane load on the axial tensile fatigue strength of the structure. At the same time, a new structural fatigue life prediction method considering out-of-plane loads is established by combining finite element analysis, which can more accurately predict the structural fatigue life under the influence of out-of-plane loads and provide support for metal structure fatigue analysis.

Enhanced Crashworthiness Parameters of Nested Thin-Walled Carbon Fiber-Reinforced Polymer and Al Structures: Effect of Using Expanded Polypropylene Foam

The in-plane loading conditions of carbon fiber/epoxy composite (CFRP) and aluminum nested-tube-reinforced expanded polypropylene (EPP) blocks were empirically examined. This study used crashworthiness metrics to estimate the best design configuration under quasi-static loading rates. The experimental phase began with lateral loading testing of single and nested aluminum and CFRP specimen. In-plane crushing experiments were performed on EPP foam blocks reinforced with nested tubes. Both single and nested aluminum tubes had comparable force–response curves and maintained their load-bearing capacity throughout testing. Despite a load-carrying capacity drop above a particular displacement threshold, the CFRP specimens had superior specific energy absorption (SEA) values due to their lightweight nature. The triple-tube nested specimens with two smaller tubes exhibited the best SEA results (1.72 and 1.88 J/g, respectively, for the aluminum and CFRP nested samples). During concurrent tube deformation, the nested samples showed a synergistic connection that increased energy absorption, especially in the EPP foam blocks with reinforced tubes. The study also examined the effects of building nested specimens with aluminum exterior tubes and CFRP inner tubes, and vice versa. This method showed that CFRP tubes within aluminum outer tubes lowered specimen weight (from 93.1 g to 67.7 g) and energy absorption (from 160.2 J to 153.3 J). However, the weight reduction outweighed the energy absorption, increasing SEA values for certain composite material configurations (from 1.72 J/g to 2.26 J/g).

Small fatigue crack behavior of CP-Ti in thin-walled cruciform specimens under biaxial loading

This study investigates the small fatigue crack propagation behavior of commercially pure titanium (CP-Ti) using thin-walled cruciform specimens under in-plane biaxial loading, considering the effects of biaxial ratio and phase angle. Increasing phase angle results in more secondary cracks merging with main cracks perpendicular to the rolling direction (RD) and transverse direction (TD), a phenomenon attributed to the rise in shear stress that accelerates main crack growth. Higher loading biaxiality or a lower phase angle leads to decreased crack propagation rates and increased biaxial fatigue life. Electron backscatter diffraction (EBSD) analysis reveals that when the maximum normal stress aligns with the RD, prismatic slip primarily governs crack propagation, thereby accelerating crack propagation rates. Conversely, alignment with the TD reduces prismatic slip activity and crack propagation rates. Under equi-biaxial loading, prismatic slip activity decreases further, and crack propagation is dominated by multiple slip and twinning, consequently resulting in the slowest propagation rates. Additionally, a higher proportion of prismatic slip under high phase angle also accelerates crack propagation. Finally, incorporating Findley equivalent stress into the Chapetti model, which considers the crack length-dependent threshold effect, a highly accurate biaxial small fatigue crack propagation rate model is proposed.

A Novel Method for Analyzing Global Bifurcation and Global Hysteresis of FGM Truncated Conical Shell Structure

In the dynamic bifurcation and dynamic hysteresis of a system, our first consideration is the tiny changes in time that can lead to variations in the vector field, potentially causing the occurrence of system dynamic bifurcation and dynamic hysteresis. This paper presents a novel method for analyzing the global bifurcation and hysteresis of Functionally Graded Material (FGM) truncated conical shell structure under aerodynamics and in-plane force along meridian near internal resonances. This method involves introducing the ratio of vector fields as a periodic perturbation parameter in the system’s nonlinear second-order ordinary differential governing equations. This allows for the analysis of the nonlinear ordinary differential equations as algebraic equations, yielding algebraic expressions that only involve parameters and do not contain state variables. Subsequently, the global bifurcation set and global hysteresis set of FGM truncated conical shell structure are obtained, providing the parameters interval ranges for the stability and instability of FGM truncated conical shell structure. By utilizing MAPLE software for numerical simulation, the images of the global bifurcation set and global hysteresis set about the amplitude of in-plane load are first simulated numerically. Subsequently, the amplitude graphs of the equilibrium points are numerically simulated for validation. The results demonstrate a perfect alignment between the images of the global bifurcation set and global hysteresis set and the data from the amplitude graphs of the equilibrium point. Due to the periodicity of the periodic perturbation parameter, it shuttles between different persistent regions as other parameters change, leading to the generation of chaotic solutions in the governing equations. The validity of the obtained results is confirmed through comparisons with existing literature.

Analytical parametric analysis of profiled composite walls reinforced with embedded tubes subjected to axial loading

This paper presents analytical analysis of the axial load behavior of a profiled composite wall (PCW) consisting of two profiled steel sheets (PSSs) filled with concrete and reinforced with/without embedded cold-formed steel tubes (CFSTs). This type of composite wall was designed to resist in-plane axial loading (bearing wall). Three experimental samples were tested and its results were presented in this research. The ultimate axial loads of 42 PCW FE models were calculated based on a published work done by the authors earlier. Comparisons between the results of the FE models via the proposed methods and those of Eurocode 4, BS5400, AISC, Hossain (2000), and Wright (1998) were made. Applied calculation formulas for the ultimate axial load were presented via regression analysis theory on the basis of the verified FE results. Comparisons were made between the developed formulas and existing experimental tests, such as those of Hossain (2000) and Wright (1998) and an experimental study performed by the author, and perfect accuracy was achieved. The results of this study proved that the effects of the embedded CFSTs reduced local buckling of the PSS and increased ductility with increasing axial load resistance of the PCW. The provided formulas accurately predict the axial load of the PCWs.

Seismic experiment and performance analysis on embedded optimized steel plate-reinforced concrete composite shear wall under multi-dimensional loading

In order to investigate the seismic performance of reinforced concrete shear walls under multi-dimensional loading mode and its effect on performance improvement, an embedded optimized steel plate-reinforced concrete composite shear wall is proposed. Based on the design principle that the shear wall could adequately bear multi-dimensional loading and the embedded steel plate could reach the full stress state, the X-shaped optimized steel plate (for in-plane loading mode) and the triangular optimized steel plate (for out-of-plane loading mode) are determined using different optimization methods. The combination scheme of these two plates is utilized in the oblique loading mode. Quasi-static loading tests are conducted on eight typical shear wall specimens, and performance parameters such as hysteresis curve, skeleton curve, ductility, stiffness degradation, strain evolution, and damage evaluation of the specimens are compared and analyzed. In addition, variable parameter analysis is performed using finite element software to compare the strain distribution state of each steel plate. The results indicate that the embedded optimized steel plate-reinforced concrete composite shear wall structure exhibits higher bearing capacity, greater deformation capacity, and superior energy dissipation capacity under different loading angles compared to the tradition reinforced concrete shear walls. This composite structure can provide greater lateral stiffness, and the optimized steel plate can reach the full stress state at all loading angles, effectively reducing the damage of steel bars and concrete. These findings offer a foundation for the study of seismic performance and performance improvement methods for shear wall structures under multi-dimensional earthquake action.

Effect of crossing warp arrangements on delamination resistance of 3D woven composite T-joints under in-plane tensile loading

An experimental study for investigating the delamination behaviour of 3D woven composite T-joints with weave variations and optimising weave architectures is carried out. This study involves 10 types of crossing warp architectures at the junction. Quasi-static tensile load is applied to two flanges of 3D woven composite T-joints to evaluate the in-plane mechanical performance. The crossing warp architecture effectively improves the in-plane mechanical performance. Results indicate a significant influence of crossing warp arrangements on failure modes of the 3D woven composite T-joints. The use of internal crossing warp architectures leads to severe delamination in the 3D woven composite T-joints while the composite T-joints with 3D woven external crossing warps primarily fail due to the debonding of fibres and matrix and fibre breakage. The optimal weave architecture for 3D woven composite T-joints is confirmed by analysing the in-plane mechanical behaviour with different crossing warp arrangements and proportions. Regardless of the crossing warp proportions, the external crossing warp architectures outperformed their internal counterparts in resisting delamination, resulting in a maximum increase of 68.75 %, 30.04 % and 116.81 % in modulus, strength and failure strain respectively.

Research into multi-directional high stability techniques in the same plane for satellite static testing

In order to ensure the structural strength reliability of spacecraft base plate during launch and operation, it is necessary to perform the structural strength test of load synchronous loading on the base plate in the same plane to evaluate its structural bearing capacity under certain axial and shear loads. In order to meet the test requirements and simulate the real stress condition of the base plate, a reliable implementation scheme is proposed in this paper. Multi-directional uniform loading of a satellite base plate is completed by using the same plane multi-directional high stability test technology. The mechanical test of a satellite using this technology shows that the test strain is consistent with the theoretical simulation deformation. This technology effectively solves the problem of uniform loading in the same plane of the satellite base plate in mechanical testing.

Deep subwavelength sound absorption by a buckling plate resonator

Conventional sound-absorbing materials face great difficulties in achieving deep subwavelength broadband sound absorption due to the causal constraint on the minimum thickness. A buckling plate resonator is proposed to alleviate the causal constraint on the thickness of sound-absorbing materials. The resonator consists of a back cavity sealed by an elastic circular thin plate. When the plate is subjected to a uniform in-plane compressive force up to its critical load, it buckles and behaves as a negative stiffness spring. The positive stiffness of the back cavity is counteracted by the negative stiffness of the buckling plate, resulting in resonance absorption at the deep subwavelength scale. The sound absorption performance of the buckling plate resonator under different in-plane loads was measured in an impedance tube. Quasi-perfect sound absorption was observed in a buckling plate resonator with a thickness less than 1% of the wavelength corresponding to the resonance frequency. This work provides a solution for the design of ultra-thin broadband sound absorbers.

Influence of in-plane transverse compression on the behaviour of the face plate component in weak axis and tubular steel joints

The behaviour of the face-plate component under out-of-plane loading has been previously studied, and analytical formulations characterizing the initial stiffness have been proposed. However, research investigating the response of this component under simultaneous transverse loading is limited. This study examines the influence of in-plane transverse compression on the out-of-plane behaviour of the face-plate component in weak axis and tubular beam-to-column steel joints. An experimental test campaign was conducted, covering five representative joint configurations for connections to both I-section and tubular columns. Finite element models of the tested specimen were generated and validated based on the test results. Subsequently, these results were supplemented by two sets of numerical parametric studies, encompassing a total of 329 connections under different levels of transverse loads. The results indicate the detrimental effect of transverse compression on the stiffness and resistance of the face-plate component. Analytical expressions for the reduction of initial stiffness under compressive in-plane transverse loads were proposed and validated, facilitating easy incorporation into design standards.

A quadrilateral inverse plate element for real-time shape-sensing and structural health monitoring of thin plate structures

The inverse finite element method (iFEM) emerged as a powerful tool in shape-sensing and structural health monitoring (SHM) applications with distinct advantages over existing methodologies. In this study, a quadrilateral inverse-plate element is formulated via a sub-parametric approach using bi-linear and non-conforming cubic Hermite basis functions for engineering structures, which can be modeled as thin plates. Numerical validation involves dense and assumed sparse sensor arrangements for in-plane, out-of-plane, and mixed general loading conditions. iFEM analysis reveals efficient monotonic convergence to analytical and high-fidelity finite element reference solutions. After successful numerical validation, defect detection analysis is performed considering minute geometric discontinuities and structural stiffness reduction because of latent subsurface defects under tensile and transverse loading conditions. The inverse formulation successfully resolves the presence of simulated defects under a sparse sensor arrangement. The proposed inverse-plate element is accurate in the full-field reconstruction of shape-sensing profiles and reliable in defect identification and quantification in thin plate structures.

An integrated approach for prognosis of Remaining Useful Life for composite structures under in-plane compressive fatigue loading

The prognostic of the Remaining Useful Life (RUL) of composite structures remains a critical challenge as it involves understanding complex degradation behaviors while it is emerging for maintaining the safety and reliability of aerospace structures. As damage accumulation is the primary degradation indicator from the structural integrity point of view, a methodology that enables monitoring the damage mechanisms contributing to the structure's failure may facilitate a reliable and effective RUL prognosis. Therefore, in this study, an integrated methodology has been introduced by targeting the RUL and progressive delamination state via Deep Neural Network (DNN) trained with Guided wave-based damage indicators (GW-DIs). These GW-DIs are obtained via signal processing, Hilbert transform, and Continuous Wavelet Transform. This work uses GW-DIs to train and test the proposed model within two frameworks: one focusing on individual sample analysis to explore path dependency in RUL and delamination prognosis and another on an ensembled dataset to propose a generic model across varying stress scenarios. Results from the study indicate that proposed DNN frameworks are capable of encapsulating fast and slow degradation scenarios to evaluate the RUL prediction with associated delamination progress, which could contribute to ensuring the integrity and longevity of critical life-safe structures.