Static Bending Behavior Research Articles

Bending and buckling responses of organic nanoplates considering the size effect

As humanity progresses, fossil fuel reserves are being increasingly exhausted, leading to increased focus on sustainable energy alternatives. Scientists are now researching solar panels that can efficiently convert solar energy into electricity for human use. This research employs a novel third-order shear deformation theory to investigate the static buckling and static bending behaviors of organic nanoplates, marking the first instance of such an approach being used. The formulas are computed using strain gradient theory to consider the impact of the size effect, where this size effect parameter is considered in both positive and negative cases. The plate's balancing equation is derived using the notion of virtual displacement, and the analytical solution is obtained using Navier's solution. The mathematical expression for deflection and critical buckling load in this study has been validated by comparing it with previously published analytical findings. This study also includes a set of numerical calculations to demonstrate the impact of certain geometric factors and the size effect on the static bending response and static buckling of organic plates. This study aims to assist designers in developing organic plate products that demonstrate optimal functionality in real-world applications

Optimising Additive Manufacturing to Produce PLA Sandwich Structures by Varying Cell Type and Infill: Effect on Flexural Properties

The objective of this research is to optimize additive manufacturing processes, specifically Fused Filament Fabrication (FFF) techniques, to produce sandwich structures. Mono-material specimens made of polylactic acid (PLA) were produced, where both the skin and core were fabricated in a single print. To optimize the process, variations were made in both the base cell geometry of the core (Tri-Hexagon and Gyroid) and the core infill (5%, 25%, 50%, and 75%), evaluating their effects on static three-point bending behavior. Optical microscopy was employed to assess both the structure generated by additive manufacturing and the fracture modes. The findings reveal that increasing the infill, and thus the core density, enhances the mechanical properties of the structure, although the improvement is such that samples with 50% infill already demonstrate excellent performance. The difference between hexagonal and Gyroid structures is not significant. Based on microscopic analyses, it is believed that the evolution of 3D printers, from open to closed chamber designs, could significantly improve the deposition of the various layers.

Experimental study on bending fatigue performance of ambient-cured ultra-high-performance concrete thin plate with embedded steel wire mesh

Ambient-cured ultra-high-performance concrete (ACUHPC) with embedded steel wire mesh (SWM) was studied experimentally. ACUHPC-SWM thin plates having different SWM wire ratios and fatigue load stress levels were tested to clarify the effects of SWM on static and fatigue bending behavior. Subsequently, the fatigue equations for ACUHPC-SWM materials (with different failure probabilities) and reinforcement efficiency of the SWM were proposed. Finally, the reinforcement mechanism of the SWM was revealed by comparing it with ACUHPC thin plates. The results show that the inclusion of wire mesh significantly improved the cracking strength, ultimate static strength, energy dissipation performance, and fatigue ultimate strength of ACUHPC, with maximum increases of 23.63 %, 260.32 %, 940.42 %, and 196.34 %, respectively. As the wire mesh ratio increased, the improvement in fatigue ultimate strength initially increased and then decreased once the wire mesh ratio exceeded 1.884 %. The mechanism according to which SWM enhances ACUHPC involves the action of the mesh as a bridge to delay crack development and increase toughness.

STATIC BENDING RESPONSE OF COMPOSITE PLATES RESTING ON VARIABLE ELASTIC FOUNDATIONS

This article introduces a finite element approach for examining the static bending behavior of composite plates. The method considers the variable mechanical characteristics of plates and utilizes an elastic foundation with varying stiffness values. The plate's calculation expressions and equilibrium equations are derived using the new style shear deformation theory. The article uses a mesh composed of four-node rectangular components to solve the equilibrium equation. Each node in the mesh has six degrees of freedom. The solution's dependability and convergence are confirmed by comparing it with previously published findings. Based on this premise, the study presents numerical findings that examine how various geometric factors, materials, boundary conditions, and elastic foundations affect the static bending behavior of composite panels. This research is a great resource for engineers, providing excellent guidance for the design, production, and utilization of these structures in real-world applications.

A study on static bending behavior of partially elastically supported functionally graded plate with porous voids and prediction of deformation through deep learning

This research explores the static bending behaviour of functionally graded rectangular plates with porous voids. It addresses maximum deformation and static bending factors under uniform-pressure, considering variables such as porous-void distributions, full and partial elastic foundations, and edge constraints. The Rayleigh-Ritz method combined with algebraic polynomials is employed to obtain the numerical solutions. The convergence test shows computing efficiency, while the validation tests against public data and ANSYS findings verify the accuracy of the present numerical model. Additionally, this research presents a deep learning-based Artificial-Neural-Network model for deformation prediction to enhance the depth of the analysis without extensive numerical simulations.

Impact characterization of coral aggregate reinforced concrete beam: A 3D numerical study

Coral aggregate concrete (CAC), an innovative construction material, utilizes abundant marine resources, including coral aggregates and seawater. In the realm of reef engineering, CAC is widely used in structural elements such as reinforced beams and columns. This paper presents a three-dimensional (3D) mesoscale model to assess the impact behavior of coral aggregate reinforced concrete beams (CARCB), incorporating the heterogeneity characteristics of CAC and the explicit simulation of reinforcement components. The 3D mesoscale modelling approach developed in this paper was validated by previous experimental data of CARCB, and used for extensive parametric studies evaluating effects such as concrete strength grade, reinforcement ratio, and impact velocity on the static and dynamic bending behaviors of CARCB. Finally, based on the mesoscopic cracking process and damage patterns of CARCB under static and dynamic loads, this study illustrates the corresponding macroscopic mechanical behaviors and failure mechanisms. Results indicate that the predominant forms of flexural failure in CARCBs are tensile cracking in the mid-span region and diagonal shear cracking. Results demonstrate that the predominant forms of flexural failure in CARCBs are tensile cracking in the mid-span region and diagonal shear cracking. Specifically, local bending failures and symmetrical diagonal shear cracks were evident in the CARCBs subjected to dynamic loads, closely resembling those in ordinary concrete beams. With increasing concrete strength grades (C30 to C60) and reinforcement ratios (0.9 %–1.7 %), a significant reduction in the mid-span ultimate deflection of CARCB is observed, indicating enhanced impact resistance. Additionally, as the impact velocity increases from 1 m/s to 50 m/s, the mid-span ultimate deflection of CARCB is magnified by a factor of approximately 200, indicating intensified dynamic damage to CARCB with increasing impact velocities.

Effects of pretension loads on bending behaviors of CFRP tendons

Carbon fiber reinforced polymer (CFRP) tendons have a high potential to replace steel ones in bridge structures. However, concerns have been raised about their poor transverse properties, particularly when CFRP tendons experience combined tensile and bending loads, as in externally pre-stressed structures. This paper aims to understand and predict the bending behaviors of CFRP tendons with a pretension load. The experiment investigated the static bending behaviors of the CFRP tendon with pretension ratios ranging from 0 to 0.6. The pretension load stiffens the bending behavior of CFRP tendons, and a lower pretension ratio leads to an obvious increase in both the maximum bending load and energy dissipation. An analytical model was proposed to predict the load-deflection relationship and threshold pretension ratio of CFRP tendons under combined tensile and bending loads. The proposed model is in good agreement with the experimental results.

A Four-Variable Shear Deformation Theory for the Static Analysis of FG Sandwich Plates with Different Porosity Models

This study is centered on examining the static bending behavior of sandwich plates featuring functionally graded materials, specifically addressing distinct representations of porosity distribution across their thickness. The composition of the sandwich plate involves a ceramic core and two face sheets with functionally graded properties. Mechanical loads with a sinusoidal distribution are applied to the sandwich plate, and a four-variable shear deformation theory is employed to establish the displacement field. Notably, this theory involves only four unknowns, distinguishing it from alternative shear deformation theories. Equilibrium equations are derived using the virtual work concept, and Navier’s method is applied to obtain the solution. The study addresses the impact of varying porosities, inhomogeneity parameters, aspect ratios, and side-to-thickness ratios on the static bending behavior of the sandwich plates. The influence of various porosities, inhomogeneity parameter, aspect ratio, and side-to-thickness ratio of the sandwich plates are explored and compared in the context of static bending behavior. The three porosity distributions are compared in terms of their influence on the bending behavior of the sandwich plate. The findings indicate that a higher porosity causes larger deflections and Model A has the highest central deflection. Adopting the four-variable shear deformation theory demonstrated its validity since the results were similar to those obtained in the literature. Several important findings have been found, which could be useful in the construction and application of FG sandwich structures. Examples of comparison will be discussed to support the existing theory’s accuracy. Further findings are presented to serve as benchmarks for comparison.

A re-look into the modeling aspects of Eringen’s strain-driven nonlocal Euler-Bernoulli nanobeam bending problems

There has long been debate on the applicability of Eringen’s strain-driven nonlocal model to the study of nanostructures. Previous studies based on Eringen’s differential and integral nonlocal models to simulate the static bending behavior of nanobeams have shown shortcomings in nanobeam elastostatics solutions. The solution methodologies employed to solve the differential and integro-differential equations arising from Eringen’s strain-driven nonlocal constitutive model have shown inconsistencies in ensuring the fulfillment of essential and natural boundary conditions. This study aims to conduct an in-depth investigation of the modeling aspects of Euler-Bernoulli nanobeams under different loading and boundary conditions. Dirac-delta identity and generalized functions-based approach shall be utilized for the same. A rigorous mathematical proof establishing the equivalence between Eringen’s differential and integral nonlocal models is presented here for the first time.

A generalized functions based approach for stress-driven nanobeam bending problems subjected to point loads

The research community has widely accepted the stress-driven nonlocal integral model to study static and dynamic characteristics of nanostructures. Although closed-form solutions for stress-driven point-loaded nanobeam bending problems that find potential for applications in the design of real-world MEMS/NEMS-based sensors have been explored recently, the static bending behavior of stress-driven Bernoulli-Euler and Timoshenko nanobeams subjected to point-loading conditions in various end configurations are studied in the present work wherein, analytical solutions for the same are arrived at by expressing the input bending and shear fields in terms of generalized functions for the first time. Equipped with the Helmholtz bi-exponential kernel function to model the nonlocality, the obtained solutions have demonstrated their ability to capture size-effects consistently. An overall stiffening effect on the nanobeam is observed as a consequence of these size-effects.

An improved FSDT with an efficient mesh-free approach for nonlinear static analysis of FG-GOPRC beams

The aim of this paper is to enhance the First Shear Deformation Theory (FSDT) beam and apply it to investigate the linear and nonlinear static bending behavior of beams containing functionally graded graphene oxide powder-reinforced composite (FG-GOPRC). In this study, we propose an improvement to the FSDT by utilizing a high-order mesh-free approach. Unlike some existing FSDT methods, our proposed study uses a nonlinear shear deformation term coupling, which is crucial to illustrate the effect of nonlinear cases of various boundary conditions under a strong formulation, even without selective or reduced integration, resulting in lower computation costs. Using the principle of minimum potential energy, the governing equations are rewritten in a matrix–vector strong form and discretized using the Radial Point Interpolation Method with variable shape parameter (VS-RPIM) and linearized using a High Order Path Following Techniques (HOPFT). To account for the behavior of GOPRC, we utilized the modified Halpin–Tsai model to estimate the effective Young’s modulus, while the rule of mixture was employed to determine the effective Poisson’s ratio. Furthermore, the weight fractions of the graphene oxide powder (GOP) vary continuously through the thickness direction of the composite beams. To validate the proposed numerical model, we provide various comparison studies to demonstrate its robustness and accuracy. Additionally, we conduct parametric studies to examine the effects of different parameters, such as length-to-thickness ratio, GOP distribution patterns, weight fraction, and size of GOP, types of loads, and boundary conditions on the nonlinear bending behavior of FG-GOPRC beams. We also investigate the neglected term in some literature, which is of interest in our study. In summary, this paper proposes an enhanced FSDT to investigate the nonlinear static behavior of FG-GOPRC beams. The proposed model is validated through various comparison studies and parametric analyses, demonstrating its robustness and accuracy. Our study provides useful insights into the nonlinear bending behavior of FG-GOPRC beams and highlights the importance of nonlinear shear deformation term coupling.

Nonlinear static bending and dynamic behaviors of graphene platelets reinforced dielectric porous arches

This paper comprehensively investigates the electro-induced nonlinear static bending and vibration behaviors of the graphene platelets reinforced dielectric porous (GPLRDP) arches. The effective dielectric permittivity and Young's modulus of GPLRDP composites are determined based on the effective medium theory (EMT). The nonlinear governing equations for the GPLRDP arch under the electrical voltage are derived by using the Hamilton principle and are numerically solved by utilizing the differential quadrature method (DQM) together with an iterative scheme to obtain its electro-induced nonlinear static bending and dynamic responses. The influences of the porosity, GPL concentration, boundary condition, central angle, and DC and AC voltage on the nonlinear behaviors of the GPLRDP arch are discussed in detail. It is found that the addition of GPLs has significant effects on the electro-induced mechanical behaviors of the GPLRDC arch when the GPLs weight fraction exceeds the percolation threshold. Numerical analysis proves that the electro-induced static and dynamic behaviors of the GPLRDC arch can be designed and actively tuned through adjusting material and structural parameters, providing valuable insights for the development of smart GPLRDP arches.

Finite-Element Modeling for Static Bending Analysis of Rotating Two-Layer FGM Beams with Shear Connectors Resting on Imperfect Elastic Foundations

The static bending of rotating two-layer functionally graded material (FGM) beams with shear connectors resting on imperfect elastic foundations was performed for the first time in this study. Timoshenko beam theory and the finite-element method are used to derive finite-element formulations. The precision of the current approach and mechanical model is shown by comparing the calculated findings of this study to those of previous precise papers. A wide variety of parameter studies are carried out to capture the impact of geometric and material characteristics on the structure’s static bending behaviors, such as the distance d, rotational speed, volume fraction index, elastic foundation parameters, and boundary conditions. This paper’s theory and mechanical models are fascinating since mechanical systems involving rotational motion are pretty standard in engineering practice. Therefore, the computed results of this work aim to contribute to our understanding of structures of this kind.

3D static bending analysis of functionally graded piezoelectric microplates resting on an elastic medium subjected to electro-mechanical loads using a size-dependent Hermitian C 2 finite layer method based on the consistent couple stress theory

Based on the consistent couple stress theory (CCST), we develop a size-dependent Hermitian C 2 finite layer method (FLM) for carrying out the three-dimensional (3D) static bending analysis of a simply-supported, functionally graded (FG) piezoelectric microplate which is placed under closed-circuit surface conditions. The microplate of interest is assumed to be resting on a Winkler-Pasternak foundation and subjected to either sinusoidal or uniformly distributed electro-mechanical loads. By setting the material length scale parameter at zero and ignoring the piezoelectric and flexoelectric effects, we reduce the formulation of the Hermitian C 2 FLM for analyzing FG piezoelectric microplates to that for analyzing FG piezoelectric macroplates and FG elastic microplates, respectively. The accuracy and the convergence rate of the Hermitian C 2 FLM are assessed by comparing the solutions it produces with the exact and approximate 3D solutions of FG piezoelectric macroplates and FG elastic microplates reported in the literature. Because the Hermitian C 2 FLM requires that the first-order and second-order derivatives of the primary variables must be continuous at each nodal plane, which in turn leads to their solutions converging rapidly and being able to obtain the accurate results of the electric and elastic variables induced in the microplates, especially for the transverse shear and normal stresses and the electric displacements. The effects of piezoelectricity, flexoelectricity, and the material length scale parameter on the deformations and stresses induced in the FG piezoelectric microplates are significant. Highlights A CCST-based Hermitian C 2 finite layer method (FLM) is developed for analyzing functionally graded (FG) piezoelectric microplates. The current FLM can be reduced to that for analyzing FG elastic microplates by ignoring the piezoelectric and flexoelectric effects. The current FLM can be reduced to that for analyzing FG piezoelectric macroplates by setting the material length scale parameter at zero. Implementing the current FLM reveals that its solutions converge rapidly and are in excellent agreement with those obtained using the exact 3D models. The effects of piezoelectricity, flexoelectricity, and the material length scale parameter on the static bending behavior of FG piezoelectric microplates are significant.

Bending performance of nail-laminated bamboo-timber panels made with glubam and fast-grown plantation Chinese fir

This study attempts to develop a novel structural nail-laminated panel constructed of engineered bamboo and local fast-grown plantation Chinese fir. An experimental program is reported in this paper on static bending behaviors of such nail-laminated bamboo-timber (NLBT) panel. Twelve NLBT specimens, including five short span specimens without butt joints and seven long span specimens with different butt joints were manufactured and tested. The panel span, species of sawn timber boards, the cross sectional configuration, and reinforcement measures of butt joints were chosen as the experimental parameters in the current investigation. The typical failure mode of the short span NLBT panels exhibited a multiple-fracture process caused by the tension failure of timber layers, while the overall collapse was much delayed or avoided attributed to the residual bending capacity provided by glubam layers. Test results demonstrate that the use of fast-grown Chinese fir instead of imported dimension lumber to combine glubam does not obviously reduce the bending performance of NLBT panels. The proposed vertical nailing reinforcement for butt joints can significantly improve the bending stiffness of the long span NLBT panels, and it is convenient for processing and assembling of NLBT components. Based on the ratio of bamboo and timber, a simple linear relationship is proposed for predicting the elastic modulus of the NLBT through regression analysis. The observed performance evaluation also reveals that the bending performance of the proposed NLBT structural panels is sufficient to meet the design requirements for using as the structural floors in offices and residential buildings. This research provides a feasible and reasonable approach for developing local fast-grown species as structural components.

Computational Modeling and Parametric Analysis of SMA Hybrid Composite Plates under Thermal Environment.

This paper presents a coupled thermoelastic finite element formulation for static and dynamic analysis of composite laminated plates with embedded active shape memory alloy (SMA) wires, which accounts for both the phase transformation and the nonlinearity effects of SMA wires. The equations of motion are obtained by using Hamilton's principle and first-order shear deformation theory (FSDT). Furthermore, based on Brinson's one-dimensional phase transformation constitutive law, a novel coupled thermoelastic finite element model that enables analysis of the SMA hybrid composite (SMAHC) plate is developed. The accuracy and efficiency of the developed computational model for analysis of SMAHC plates are reinforced by comparing theoretical predictions with data available from the literature. The results of the numerical examples also show the ability of the proposed model to predict the thermal-mechanical behavior of SMAHC plates in accordance with SMA's hysteresis behavior. In addition, based on the proposed model, the influence of temperature as well as SMA volume fraction, pre-strain value, boundary condition and layup sequence on the static bending and free vibration behavior of the SMAHC plates is investigated in detail. The results of parametric analysis show that the variations of both static deflection and natural frequency of the SMAHC plate over temperature exhibit a nonmonotonic behavior.

Modeling Static and Dynamic Bending Behavior of Soft Pneunets

Robotic grippers are widely used in industry to automatically handle specific products. While traditional rigid manipulators are often designed task-specifically, soft grippers with their compliant behavior have been proposed to flexibly handle a range of products with various shapes and materials. One sort of such soft grippers are pneumatic networks (short: pneunets). When pressurized, pneunets can perform different movements (e.g. linear or bending) depending on their design. Due to the nonlinear properties of their soft materials, linear models are not able to accurately describe pneunets’ bending behavior. Thus, non-linear models are necessary for controlling pneunets.In this work, additively manufactured (fused filament fabrication (FFF)), unidirectional pneunets are tested regarding their bending behavior while being pressurized. The pressure is applied in a staircase function (up and down), where each step is held long enough to observe the static behavior of the system. ArUco markers are used to track the pneunets’ bending behavior regarding x- and y-coordinates as well as orientation of the last chamber. With this data, nonlinear dynamic models, namely temporal convolutional networks (TCNs), are trained. In order to produce a static characteristic of this system that maps the input to the output, quasi-static behavior is simulated with the trained dynamic models.The output of the dynamic model is compared with the observed results regarding static and dynamic behavior. The comparison shows that TCNs are suitable for modeling the deflection behavior of pneunets. However, for higher pressure levels deviations are noticed. In future research, the applicability of TCNs for modeling pneunets’ long-term deflection behavior should be investigated.

Fatigue and Failure Analysis of Sandwich Composites using Two Types of Cross-Ply Glass Fibers Laminates and Epoxy Resin

Sandwich structures have become effective structural elements for engineering applications due to their good design flexibility. Understanding the material behavior under static and dynamic loads, as well as the failure mechanisms of these sandwich structures, is of great importance. This work evaluates the fatigue and static bending behavior of epoxy resin specimens and sandwich composites composed of an epoxy resin core with glass fiber laminated faces. The fatigue life, failure modes, and stiffness degradation of these specimens are determined experimentally. The specimens were cycled under constant amplitude and monitored by a data acquisition system that allowed continuous data collection. Three stages of failure were identified using microscope analyses and stiffness degradation curves. In the case of an imposed displacement of 2 mm, the sandwich structures were shown to have a significantly lower fatigue life than the epoxy resin specimens.

Investigate the bending and free vibration responses of multi-directional functionally graded plates with variable thickness based on isogeometric analysis

This study investigates the static bending and free vibration behaviour of Multi-directional Functionally Graded (MFGM) plates having a variable thickness. With this regard, the third-order shear deformation plate theory is used to describe the kinematic relation. Material properties of MFGM are assumed to be graded in spatial direction within the plate’s volume and the effective material properties are calculated based on the power-law approach. The governing equations are derived based on Hamilton’s principle and the Isogeometric Analysis (IGA) is employed as a discretization tool to develop system equations. Several numerical examples are conducted to verify the accuracy of the proposed approach and investigate the influence of different geometrical and material parameters on the behaviour of MFGM plates

Response analysis of functionally graded piezoelectric plate resting on elastic foundation under thermo-electro environment

The paper investigates the static, bending and vibration responses of the functionally graded piezoelectric plate (FGPP) resting on the two/three-parameter foundation under a thermo-electro environment. Hamilton’s principles are used with first-order shear deformation theory to obtain the governing equations. They are solved using nine noded interpolation functions with 63 degrees of freedom (DOFs) per element. It is observed that the two-parameter foundation has a shear layer dominant, and the three-parameter foundation has an additional layer of spring that plays a significant role in the static bending and vibrational behavior of the CB/UCB conditions FGPP. The applied electrical voltage and the temperature change affect the static bending, and vibrational results as the rise in temperature lead to the plate’s softening. An increase in voltage leads to a reduction in the stiffness of the plate. Also, Sg-law significantly influences the dimensionless frequency, center deflection, and axial stress compared to other laws.