•A new hyperbolic shear deformation theory is devoted for the static analysis of functionally graded plates.•An effective numerical approach is also developed to combine the proposed RPT and IGA for ...the static bending analysis of FG plates. The hyperbolic function has more general form than the classical polynomial.•IGA using the NURBS approximation functions can tower over the FEA and can easily solve the C1-continuity problem required for RPT.
A new refined plate theory (RPT) combined with isogeometric analysis (IGA) is proposed for the static and buckling analysis of functionally graded plates (FG plates). The proposed theory uses a new hyperbolic distributed function to describe the distribution of the shear strains and stresses through the plate thickness. It satisfies the shear stress free boundary conditions, so that it does not require shear correction factors. Compared with the higher-order shear deformation theories (HSDTs), the proposed RPT needs only 4 unknown variables, which improves the computational efficiency. The NURBS approximation functions built for proposed theory can easily solve the C1-continuity problem required by RPT. The material properties of the FG plates can be obtained by the rule of mixture and Mori-Tanaka technique. The static bending and buckling analysis results of different FG plates are given, and the effects of the material index n and width-to-thickness ratios on the static bending and buckling behavior of FG plates under different boundary conditions are investigated numerically.
•A unified nonlocal strain gradient beam model with the thickness effect is developed.•Analytical solutions for the bending of hinged-hinged beams are obtained.•Size effect can be not only ...length-dependent but also thickness-dependent.•The generalized Young’s modulus depends on applied load types.•The coupling of the shear and thickness effects needs be drawn attention.
A unified nonlocal strain gradient beam model with the thickness effect is developed to investigate the static bending behavior of micro/nano-scale porous beams. Size-dependent governing equations and corresponding analytical solutions for the bending of hinged-hinged beams are obtained by employing minimum total potential energy principle, the Navier solution method as well as the variational-consistent boundary conditions. For nonlocal strain gradient theory (NSGT) with thickness effect, virtual strain energy function of shear beams can contain additional nonlocal shear stress and high-order nonlocal shear stress related to the thickness direction in comparison with that of Euler–Bernoulli beam, so the coupling of the shear and thickness effects should be drawn huge attention. By means of detailed numerical analysis, it is found that, the stiffness-hardening effect is underestimated in NSGT without the thickness effect, and the stiffness-hardening and stiffness-softening effects of NSGT with the thickness effect can be not only length-dependent but also thickness-dependent. Interestingly, the generalized Young’s modulus depends on half-wave number, which means that the generalized Young’s modulus may be different due to applied load types. In the context of NSGT with the thickness effect, the deflection of Euler–Bernoulli beam predicted is smaller than that of shear beam, especially for thick beams. Furthermore, porosities distributed in the top or bottom of beams can possess a greater influence on the decrease of overall stiffness of beam than those distributed in the vicinity of the middle plane of beams.
•Flexural experiments were conducted on composite beam specimens between high-strength steel with nominal yield strength of 690 MPa and ultra-high-performance concrete (UHPC) with cubic compressive ...strength of 140 MPa.•The effects of the degree of shear connection and layouts of the studs on flexural performance of high-strength steel—UHPC composite beam were investigated.•Finite element analysis was conducted to compare the influence on flexural performance of composite beam between UHPC and normal concrete.
High-strength structural steel (HSS) and ultra-high-performance concrete (UHPC) are materials countries hope to use in civil engineering construction. This study investigated the static bending performance of HSS-UHPC composite beams through experiment and finite element analysis. First, four static bending tests were conducted. The test parameters included the degree of shear connection and the arrangement of studs (single-stud and group-stud arrangement). The group-stud arrangement was applicable for the assembly construction, which developed increasing fast in civil engineering. The experimental results showed that the failure mode of the composite beam with partial shear connection was stud fracture caused by an insufficient number of studs to withstand the shear force on the steel–concrete interface; for the composite beam with full shear connection, the failure mode was the crushing of the UHPC slab at the loading point. The deflections at mid-span for both the single-stud and group-stud specimens were the same in the elastic stage. However, the deflection of the group-stud specimen was greater than that of the single-stud specimen in the plastic stage. The results showed that the bending stiffness of the composite beam with studs arranged in a group decreased faster. Under the same load, the steel–concrete interfacial slip of the group-stud specimen was also greater than that of the single-stud specimen. Finally, this study compared the mechanical properties of the Q690-UHPC and Q690-normal strength concrete C60 (NSC60) composite beams through finite element analysis. It was found that under the same deflection, the damage of the normal strength concrete slab was more substantial than that of the UHPC slab. The bending stiffness and ultimate bending capacity of the Q690-UHPC composite beam were greater. Q690 HSS had better material strength matching with UHPC than that of normal strength concrete C60.
Based on the flexoelectric theory incorporating strain gradient and polarization gradient, a flexoelectric curved microbeam model is established. The governing equations, boundary conditions and ...initial conditions are derived by Hamilton's principle. Both the static bending and natural vibration problems are solved. The direct and converse flexoelectric responses are numerically analyzed. In the direct flexoelectric response, more collected charges are expected in the beam with larger original curvature for simply supported boundary, but the opposite is true for clamped boundary. In the converse flexoelectric response, the voltage-induced bending exists even in a clamped curved beam while it is not the case for a clamped straight beam and larger original curvature always implies larger deflection for both boundary conditions. In addition, the strain gradient elastic effect is found to reduce both the flexoelectric responses especially when the thickness is comparable to the length scale parameter associated with strain gradient.
In this paper, a refined hyperbolic tangent higher order shear deformation theory is developed. Assuming that the shear function is parameter dependent, the parameters are determined by the inverse ...method. The refined theory is assessed by using the NURBS based isogeometric analysis for the geometric linear and nonlinear bending and free vibration problems of laminated composite plates. The nonlinearity of the plates is based on the von-Karman strain assumptions. Numerical examples show that the refined hyperbolic tangent shear deformation theory combined with IGA has high accuracy in both linear and geometric nonlinear analysis of laminated composite plates. The effects of plate length–thickness ratio, modulus ratio and stacking sequence on the static bending and free vibration behaviors of laminated plate are also discussed.
•A new refined hyperbolic tangent higher order shear deformation theory is developed.•The geometric linear and nonlinear bending and vibration sogeometric analysis of laminated composite plates is performed.•The plate thickness and selection of plate theory have significant influence on the nonlinearity of bending deflection.•The mode switching phenomena occurs with the increment of vibration amplitude, and is affected by many factors.
Although the auxetic structure exhibits excellent mechanical properties, the low stiffness, and strength still limit its development. Considering the high stiffness and strength of the sandwich ...structure, a novel sandwich beam with an enhanced auxetic core (SCH SWB) was proposed in this paper. The accuracy of the finite element (FE) modeling was first verified by quasi-static bending experiments. Then, based on FE simulation, the deformation modes and energy absorption were explored. The results showed that local indentation and global bending deformation coexisted under the mid-span loading, and the core can absorb the most energy. Furthermore, using the analogy method, and based on the yield criterion and indentation response of the foam sandwich beam, a theoretical model was established to predict the force response, which considered the influence of local indentation on the overall bending, and the double-plateau characteristic of the auxetic core. The theoretical results were basically consistent with the simulation. Subsequently, the influence of the key parameters of the core and faces on the mechanical responses was discussed in depth, and it was found that changing the key geometric parameters and the material combination of the faces and the core can significantly vary the energy absorption capacity. Finally, several sandwich beams with different auxetic cores were compared, and the results proved that SCH SWB exhibited superior bending resistance and higher energy absorption. This paper presents a new idea and theoretical basis for studying the mechanical response of auxetic sandwich beams. The results show that the auxetic sandwich beam has great potential in aerospace, automobile crash, impact protection of key engineering structures, etc.
•A novel sandwich beam with an enhanced SCH auxetic core was proposed and investigated.•The global bending and local indentation were co-exist under quasi-static concentrated loading.•A theoretical analytical model was firstly established to predict the mechanical response of the beam under fixed boundary.•The contribution of the core on the energy absorption was higher than the top/bottom faces.•The SCH sandwich beam exhibited better bending resistance TEA and SEA capacity compared other common auxetic sandwich beam.
•The quasi-static bending mechanical behavior of ARG-TRC-SPs is identified.•The mix failure of face-sheet bending fracture and core shear is the most common.•Increase the reinforcement layers and ...ribs is beneficial for the properties.•The core thickness of TRC-SP has a suitable thickness.•The theoretical predictions were consistent with the test results.
A sandwich panel was prepared with Alkali Resistant-glass textile reinforced concrete (ARG-TRC) as the face sheet and Expanded Polystyrene (EPS) granular mortar as the core in this paper. Afterward, a quasi-static bending test was conducted to investigate the influences of the number of reinforcement layer, core thickness, and interface rib on the bending behaviors and failure of ARG-TRC sandwich panels (ARG-TRC-SPs). On this basis, the elastic bending deformation and ultimate bending capacity were theoretically predicted, and the failure mechanism was analyzed. The results show that ARG-TRC-SPs exhibited three common failure modes: face sheet bending fracture, core shear, and core crushing. Increasing the reinforcement layers significantly improved the properties of ARG-TRC-SPs but decreased textile utilization. Although the enhancement of the interface rib was dependent on the number of reinforcement layers, it could improve the integrity of ARG-TRC-SPs. There was a suitable core thickness for the ARG-TRC-SPs, and a thicker core did not indicate better mechanical properties. The theoretically predicted elastic deformation and ultimate bending capacity were in good agreement with the test results. However, the contribution of the core and interface ribs was underestimated. These results can provide a valuable reference for researchers and engineers in designing and applying TRC-SPs.
Flexoelectricity is the phenomenon of electric polarization caused by the strain gradient, which usually has a huge effect on nanoscale structures. This paper firstly combines the finite element ...method (FEM) with a novel third-order shear deformation beam theory (TSDT) to simulate the static bending and free vibration responses of rotating (around one fixed axis) piezoelectric nanobeams with geometrical imperfection considering flexoelectric effects, where the structures are placed on the Pasternak’s elastic foundations. Based on two-node beam elements, the Lagrange and Hermit interpolation functions, the proposed approach shows high accuracy through the comparative results of this work and published references. A wide range of parameter studies is conducted such as the rotational speed, shape imperfection, flexoelectric effect, and so on to evaluate the influences on the static bending and free vibration behaviors of the structures. The novel investigation points out that when the beams are rotating around one fixed axis, the mechanical responses, in this case, are not similar to those of normal cases when the rotational speed is zero. This is a new study that can be referenced when designing nanoscale beam structures in practice.
Abstract
Due to its remarkable physical features, graphene nanosheets (GPN) are one of the most appealing reinforcing materials for composites. For polyvinylidene fluoride (PVDF), GPN reinforced ...composites can dramatically increase its piezoelectric and mechanical characteristics. If the interlaminar shear deformation of laminated plates containing uniform graphene sheets reinforced (GSR) smart piezoelectric layer, which material properties vary widely from layer to layer and subjected to electromechanical loading cannot be accurately predicted, the interlaminar stresses may be very high, eventually leading to interlaminar failure. In light of this, an effective mechanoelectrical coupling model for the accurate prediction of interlaminar stress for composite plates contains GSR actuators is developed in present study. Meanwhile, the finite element formulation (FEF) can be substantially simplified due to the expression of transverse shear stress components becoming more succinct. Therefore, by using the suggested electro-mechanical coupling theory, a three-node FEF is easily constructed. The refinement of transverse shear stress prediction in the context of electromechanical coupling can be accomplished through the application of the Reissner mixed variation theory (RMVT). The performance of the recommended plate model will be evaluated using the results derived from three-dimensional (3D) elastic theory and the selected model. By employing the RMVT method, we improve predictions of transverse shear stresses while considering the electromechanical coupling effect. The results from our model are compared with alternative models and 3D elasticity theory, demonstrating its superiority in satisfying the continuity requirements of transverse shear stresses and exhibiting excellent agreement with exact solutions. This validates the accuracy and applicability of our proposed model. Further to that, the prediction of mechanical characteristics for laminated plates with GSR actuators were systematically studied from the thoroughly perspectives of electromechanical load, piezoelectric layer thickness, graphene volume fraction, and some other parameters.
The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous (FGP) variable-thickness plates by using an edge-based smoothed ...finite element method (ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element (MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index (k) and maximum porosity distributions (Ω) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.
PDF