In-plane Forces Research Articles

Investigation of Metal Wire Mesh as Support Material for Dieless Forming of Woven Reinforcement Textiles

Within the rapidly growing market for fiber-reinforced plastics (FRPs), conventional production processes involving molds are not cost-efficient for prototype and small series production. Therefore, new flexible forming techniques are increasingly being researched, many of which have been inspired by incremental sheet metal forming (ISF). Due to the different deformation mechanisms of woven reinforcement fibers and metal sheets, ISF is not directly applicable to FRP. Instead, shear and bending of the fibers need to be realized. Therefore, a new dieless forming process for the production of FRP supported by metal wire mesh as an auxiliary material is proposed. Two standard tools, such as hemispherical punches, are used to locally bend a reversible layup of metal wire mesh and woven reinforcement fiber fabric enclosed in a vacuum bag. Therefore, the mesh aids in introducing shear into the material due to its ability to transmit compressive in-plane forces, and it ensures that the otherwise flexible fabric maintains the intended deformation until the part is cured or solidified. Basic experiments are conducted using thermoset prepreg, woven commingled yarn fabric, and thermoplastic organo sheets, proving the feasibility of the approach.

Analytical solutions for buckling analysis of cracked plates under in-plane compressive loads: 2D refined modeling

Two refined two-dimensional (2D) crack models are developed to deal with rectangular isotropic and orthotropic plate problems with all-over part-through surface cracks under in-plane compressive loads. In the refined models, the crack terms are directly incorporated into the governing equations of cracked plates. In particular, the effect of internal in-plane forces can be investigated by theoretical analysis. The critical buckling loads of thin plates with uni-directional or bi-directional part-through cracks under uni-axial or bi-axial compressive loads can be determined analytically. In this work, different material properties, including steel, tempered glass, glass-fibre-reinforced composite, and graphite-epoxy composite, are considered. The influence of crack depth ratio and plate aspect ratio on the critical buckling loads of these structures is also presented. The analytical results are compared with those results obtained by the line-spring model and three-dimensional finite element method to verify their correctness and accuracy. The proposed models are highly effective for the buckling analysis of plates with part-through cracks.

Structure cladding interaction in sandwich panel roofs

A few years ago, several failures in the sandwich panel cladding systems of large warehouses or distribution centres (“Big Sheds”) in the UK highlighted shortcomings in the current design philosophy, which ignores the global effect of cladding on the performance of the structure. The current European Standard for including the effect of cladding (i.e., diaphragm action) in the structural analysis is inappropriate for modern cladding systems, especially in association with ultra large portal frame structures.In this paper, a new state-of-the-art for sandwich panels acting as a diaphragm to resist in-plane forces in portal frame structures is defined. The modern terminology for such interactive behaviour is now given the more general title of “Structure Cladding Interaction”. Potential cladding failure modes are highlighted and where possible quantified. The “component method” is advocated as the best way to include the global effects of sandwich panels in a 3D finite element model of the complete structure. Guidance on generating such models, obtaining the critical component properties and validation is provided, together with three detailed validation examples. The method is both scalable and general; it may be used to model the effects of cladding in any size of structure or of any structural form. It is strongly recommended that the influence of the cladding should be included in the design of any large portal frame structure. In such buildings the serviceability limit state is likely to be defined by cladding failures which may occur below the working loads. Detailed outcomes obtained using sophisticated 3D models will be presented in subsequent papers.

Two-dimensional orthotropic plate problems in a thermal environment: Refined crack modelling

Three two-dimensional (2D) refined models are devised for the analysis of orthotropic thin plates with part-through surface and internal cracks under in-plane forces due to temperature differences. The refined models are used to formulate the governing equations for cracked orthotropic thin plates in a thermal environment. Subsequently, the refined models and their ensuing modified forms can be directly applied to all-over and finite-length cracks, respectively. Using an interface-fitted numerical scheme (i.e., matched interface and boundary technique), the resulting equations of motion for the buckling and free vibration of cracked orthotropic thin plates are solved. The effects of various crack types and dimensions on the critical buckling temperatures and vibration frequencies of orthotropic thin plates are investigated. The present models are also validated by comparing their numerical results with the line-spring model and three-dimensional finite-element solutions. Illustrative examples, including boron fiber/epoxy and glass-fibre-reinforced composite materials, are considered to show the superiority of the proposed models over the conventional one, especially in terms of understanding the effect of in-plane forces arising from temperature differences at the cracked location.

An Experimental and Numerical Evaluation of the Aerodynamic Performance of a UAV Propeller Considering Pitch Motion

Considering the vibration generated by a propeller-driven UAV or encountering gust, the propeller will perform a very complex follower motion. A pitch and rotating coupled motion is proposed in the present work that can take more complex unsteady performance of follower force than a regular fixed-point rotating motion. In order to evaluate the unsteady follower force and conduct parametric study, an extensive ground test bench was designed for this purpose where the whole test system was driven by a linear servo actuator and the follower force was measured by a 6-component balance. For CFD simulation, coupled motion in particular needs detailed unsteady aerodynamic model; therefore, a high-fidelity CFD-based study integrated with the overset mesh method was complemented to solve the unsteady fluid of varying conditions. The results suggest that a significant influence on unsteady follower force is observed, and the mean value of in-plane force does not equal to zero during the coupled motion process. Compared with the regular fixed-point rotation of propeller, the fluctuation frequency of follower force in present work couples the rotation and pitch motion frequencies. In addition, the oscillation amplitude of out-plane force and torque is positively related with the pitch frequency, pitch amplitude, and relative length from leading edge of wing to the rotation center. For example, the oscillation amplitude of 1-blade’s out-plane force and torque increases by 57.122% and 66.542% for the 5 Hz-5 deg case compared with the 5 Hz-3 deg case, respectively. However, the torque is not sensitive to frequency of pitch motion. The generally excellent agreement evident between the ground test and numerical simulation results is important as guidance for our future investigation on “dynamic” aerodynamic performance of a propeller-driven UAV.

Analysis of RCC Building with Regular and Dumbbell Shaped Shear Wall in Different Types of Zones Using ETABS Software

Abstract: In structural engineering, a shear wall is a vertical element of a seismic force resisting system that is designed to resist in-plane lateral forces, typically wind and seismic loads. In many jurisdictions, the International Building Code and International Residential Code govern the design of shear walls. A shear wall resists loads parallel to the plane of the wall. Collectors also known as drag members; transfer the diaphragm shear to shear walls and other vertical elements of the seismic force resisting system. Shear walls are typically light-framed walls with shear panels, reinforced concrete walls, and reinforced masonry walls. The G+15 story structures situated in earthquake zones III, IV and V will be considered for study. All frames are designed under same gravity loading. Response spectrum method is used for seismic analysis. ETABS software is used and the results are compared. The results were obtained in the form of top story displacement, Story drift, Base shear and displacement

A superconvergent meshfree collocation formulation for laminated composite plates with particular focus on convergence analysis

A superconvergent meshfree collocation formulation is presented for the accurate analysis of laminated composite plates, where the convergence characteristic is particularly investigated. The shear locking is resolved through the employment of a mixed formulation that takes the in-plane displacements, deflection, rotations and shear forces as primary variables. The resulting meshfree collocation equations are attained by introducing the recursive gradients constructed from the first order gradients of meshfree shape functions. Subsequently, the convergence of both the standard meshfree collocation approach and the proposed recursive gradient meshfree collocation formulation is theoretically analyzed for the system of mixed discrete equations corresponding to laminated composite plates. These theoretical results clearly identify the basis degree discrepancy issue for meshfree collocation analysis of laminated composite plates. More importantly, this accuracy deficiency is successfully removed by the recursive gradient meshfree collocation formulation, which essentially achieves a desirable superconvergence for the meshfree laminated plate solutions. The superior accuracy and locking free performance of the present meshfree collocation formulation is thoroughly demonstrated by numerical results.

Pyrolytic Graphite for an In-Plane Force Study of Diamagnetic Levitation: A Potential Microdetector of Cracks in Magnetic Material.

The diamagnetic levitation technique can be applied in non-destructive testing for identifying cracks and defects in magnetic materials. Pyrolytic graphite is a material that can be leveraged in micromachines due to its no-power diamagnetic levitation on a permanent magnet (PM) array. However, the damping force applied to pyrolytic graphite prevents it from maintaining continuous motion along the PM array. This study investigated the diamagnetic levitation process of pyrolytic graphite on a permanent magnet array from various aspects and drew several important conclusions. Firstly, the intersection points on the permanent magnet array had the lowest potential energy and validated the stable levitation of pyrolytic graphite on these points. Secondly, the force exerted on the pyrolytic graphite during in-plane motion was at the micronewton level. The magnitude of the in-plane force and the stable time of the pyrolytic graphite were related to the size ratio between it and the PM. During the fixed-axis rotation process, the friction coefficient and friction force decreased as the rotational speed decreased. Smaller-sized pyrolytic graphite can be used for magnetic detection, precise positioning and other microdevices. The diamagnetic levitation of pyrolytic graphite can also be used for detecting cracks and defects in magnetic materials. We hope this technique will be used in crack detection, magnetic detection and other micromachines.

Experimental Study on Spring Constants of Structural Glass Panel Joints Under In-Plane Loading

Commonly, the columns and beams of glass panels are frequently subjected to in-plane loading, in which their joints will transfer the in-plane forces. Therefore, it is necessary to investigate the spring constants of the joints of these glass panels for the mechanical analysis of the structures. However, few issues were published on this subject, so estimating the spring constants of glass structure joints is important. Devote themselves to proposing methods to evaluate the spring constants of the joints of structural glass panels. This study tests two types of glass panels with thicknesses of 12 mm and 19 mm based on static and cycling loading. In addition, two types of Cushions: (1) aluminum and (2) rubber with a hardness of 65 and 90 degrees, are set between steel bolt(s) and glass panel(s) for the experiments. The spring constants are determined by the ratios of measured loads and the displacements between the glass panels and bolts. In addition, the authors proposed an equation to evaluate the bending spring constant from its axial spring constant determined by the loading tests. The experimental results showed that the joints with the aluminum cushion appear exactly non-linear elasticity while loading and unloading. Also, the pin junction within the central region (no Curve) is 0.6mm. It is also determined that aluminum (cushion) slides of approximately ±0.3mm under compression and tension. While loading (Tension/compression) is incremental, rubber acts nonlinearly but linear as unloaded.

BEM applied to the buckling analysis of skew and perforated plates considering the curvatures in the geometrical nonlinearity effect.

This study considered the effect of shear deformation in the bending model, which was important to assess of the plate buckling loads according to changes in the thickness. The buckling of square, skew, and perforated plates was studied with the rotation gradient (curvature) and the deflection gradient in the in the geometrical nonlinearity (GNL) effect using the BEM. The importance of the curvatures appeared when the thickness-to-span ratio reached 0.05 and increased for thicker plates in several cases. The present boundary elements formulation used the gradient of the displacements instead of second derivatives in the GNL, which disregarded the relation between the in-plane forces derivatives consequently. The singularities related to the differentiation process to obtain the BIEs for the gradient of displacements and for the stresses were reduced with using the tangent differential operator.

Wearable patch with direction-aware sensitivity of in-plane force for self-powered and single communication channel based human-machine interaction

The merging of flexible technologies with human machine interaction (HMI) is now optimizing the way people communicates with electrical terminals. Compared with “press” and “strain”, “sliding” is a directional operation which requires the interface to identify the directions of the applied force for accurate interaction. Previous efforts that explore the “directional force” in HMI system are mainly based on sensor array, which brings concern of complex electrode design and multiple communication channels to prevent cross-talk. In view of this, we developed a self-powered and wearable HMI interface that can distinguish the axial directions of in-plane force based on Faraday’s law of induction. The interface consists of well-orientated magnetized micropillars, and a conductive coil that collects and transmits the electrical signals during the interaction process. When in-plane sliding force was applied, distinguishable signals were generated to reflect the different axial directions (+X/−X/+Y/−Y) according to the polarity and number of voltage peaks. With this unique behavior, the HMI process can be completed with two electrodes and one communication channel in an interference-free manner. Through the systematic optimization, the intrinsic oscillation from the micropillars results in obviously enhanced signals for a high accuracy and reliability towards real application. The MMPs-based interface was successfully established for HMI platforms such as intelligent robot control, and Morse code communication, etc. Owing to the robustness, humid resistance, accuracy and reliability, we expect that the interface design can inspire the development of flexible and wearable devices in HMI especially for scenarios that require a high command capacity.

Three-dimensional vibration analysis of curved pipes conveying fluid by straight pipe-curve fluid element

A three-dimensional straight pipe-curve fluid theory is developed for the modeling of pipes conveying fluids with arbitrary configurations, and the corresponding finite-elements-based numerical approach to the nonlinear dynamics of curved pipes is proposed. Initially, the theoretical model of a straight pipe-curve fluid system is built along with its corresponding finite element. Subsequently, this proposed methodology is tested by conveying fluids through semicircular curved pipes. Coupling vibration mechanisms between in-plane and out-of-plane systems are explored. Finally, the influence of non-linear terms related to internal forces on the vibrations of curved pipes conveying fluid is discussed to simplify the theoretical model. The results provide useful insights into the subject matter: (i) The three-dimensional straight pipe-curve fluid element proposed is effective in analyzing the vibration behavior of curved pipe conveying fluid; (ii) When the parameter vibration of the out-plane frequency occurs and the pulsation frequency is about two-thirds of the out-plane second natural frequency, the in-plane and out-of-plane vibrations couple with the beat frequency; (iii) When combined vibration of out-plane first and second natural frequencies occur, in-plane and out-of-plane vibrations coupled with the out-plane first natural frequency; (iv) The main factors causing out-of-plane and coupling vibration of in-plane and out-of-plane systems are nonlinear terms related to axial force and in-plane transverse force.

Studies on shear strength and stiffness of brick masonry walls

Load bearing walls of Masonry structure are subjected to both gravity loads and horizontal loads during earthquake. The failure in shear is normally observed in masonry buildings under lateral in-plane loads. The state of knowledge relating to the strength and deformation characteristics of masonry to in-plane lateral loads is less than that in compression. The shear strength and stiffness of walls are important parameters in the design of masonry structures against lateral loads. Hence detailed investigation on the behavior of masonry when subjected to lateral in-plane forces is necessary. The shear strength and stiffness of masonry walls built with burnt clay bricks in 1:6 cement mortar and thin jointed cement granite fines paste have been evaluated from racking load test. Walls with different configurations such as with flanges, with reinforcement and both the half brick and one brick thick walls without reinforcement were built and tested. Load deflection graphs were plotted for all the walls and the shear strength, stiffness,energy for failure were determined. The results indicated that the shear strength of walls built in thin jointed masonry is superior compared to conventional cement mortar. The behavior of walls with flanges is ductile when compared to walls without flanges.

Bifurcation Point Analysis of a Magnetostrictive Sandwich Composite Plate Subjected to Magnetic Field and Axial Force

This article studies parametric vibration and dynamic instability of a rectangular and symmetric magnetostrictive sandwich composite plate (MSCP) on a visco-Pasternak medium. The MSCP consists of three layers; a magnetostrictive layer considers the core and composites as its upper and lower faces. The MSCP subjected to temperature change, parametrically exciting force, and magnetic load is studied with consideration to geometrical von Karman nonlinearity. Based on the energy method and first shear deformation theory (FSDT), Hamilton’s principle is used to achieve the system’s governing equations and boundary conditions. In the next step, the partial differential equation is transformed into ordinary differential equations by applying the Galerkin technique. Then the equation of motion is solved using the multiple-scale method. Numerical results illustrate the stability of the sandwich plate is significantly related to the magnetostrictive parameters. In addition, the effects of significant parameters, such as the effect of amplitude response and parametric excitation or detuning parameter, coupled with the effect of foundation, thickness ratio, aspect ratio, and temperature increment on vibration characteristics, bifurcation points behavior and stability of the systems are charted, plotted and discussed. The innovation of this article is the use of magnetostrictive material in sandwich plates and the development of its mathematical relationships. It is anticipated that the results of this research can contribute to the development of future smart structural applications subjected to in-plane axial forces.

Stringer-panel model to support the seismic design and response verification of building diaphragms

Diaphragms are essential structural elements of the earthquake-resisting system in a building. Diaphragms are the building slabs subjected to in-plane forces which are transferred to the vertical elements of the earthquake-resisting system. In-plane forces can arise from inertial loads and from self-equilibrating forces caused by the interaction between elements of the vertical earthquake-resisting system of different stiffness. The analysis and design of diaphragms is one of the most challenging tasks in design of buildings nowadays.This paper describes a stringer-panel model used as a macro-element for the modeling of building diaphragms in linear and nonlinear time-history analyses. The element was coded in the open-source finite element software OpenSees. The linear version of the element is first used to support the design of diaphragms in a building. Then, the nonlinear response of the diaphragms is assessed with the nonlinear version of the element.Key response parameters of diaphragms modeled with the dynamic stringer-panel method in a high-rise building of complex geometry are presented. Results show significant redistribution of internal forces occurs through the diaphragm after cracking, leading to a general reduction of the tensile forces and an increase in the compressive forces. The clear load path, computational stability, efficiency, and highly design-oriented representation of the results of this method make it an attractive alternative for its use in the modeling and design of diaphragms in performance-based seismic design.

An immersed boundary-lattice Boltzmann flux solver for simulation of flows around structures with large deformation

In this paper, we present an immersed boundary-lattice Boltzmann flux solver (IB-LBFS) to simulate the interactions of viscous flow with deformable elastic structures, namely, two-dimensional (2D) and three-dimensional (3D) capsules formed by elastic membranes. The IB-LBFS is based on a finite-volume formulation and makes use of hydrodynamic conservation equations with fluxes computed by a kinetic approach; thus, it is more flexible and efficient than the standard immersed boundary-lattice Boltzmann methods. The membrane of the 2D capsule is represented by a set of discrete Lagrangian points, with in-plane and bending forces acting on the membrane obtained by a finite difference method. In contrast, the membrane of a 3D capsule is discretized into flat triangular elements with membrane forces calculated by an energy-based finite-element method. The IB-LBFS is first validated by studying the deformation of a circular capsule in a linear Newtonian and a power-law shear flow. Next, the deformation dynamics of a spherical, an oblate spheroidal, and a biconcave capsule in a simple shear flow are simulated. For an initially spherical capsule, the tank-treading motion of its membrane is reproduced at the steady state; while for oblate spheroidal and biconcave capsules, the swinging and tumbling motions are observed. Furthermore, under certain parameter settings, the transient mode from tumbling to swinging motions is also found, showing a rich and complex dynamic behavior of non-spherical capsules. These results indicate that the IB-LBFS can be employed in future studies concerning the dynamics of a capsule suspension in more realistic flows.

Stress analysis of adhesive-bonded tubular-coupler joints with optimum-stiffness-composite adherend under axial tension, pressure, and thermal loading

With descriptions of fiber orientation variation, variable-stiffness composites (VSCs) have opened many new opportunities for structural designs because they offer tailorable material properties to increase the performance of composite structures. Using the concept of VSCs, this study aimed to determine the optimum adhesive-bonded tubular coupler joints subjected to tension, pressure, thermal load, and/or combinations thereof. The joint consists of three axisymmetric cylindrical adherends. The two inner adherends are made of a linear elastic isotropic material, whereas the outer adherend is composed of a symmetric balanced laminate. As the most complicated cases among others, owing to various stress components induced in the adherends and adhesive, the joints under these dominant in-plane normal force loadings are modeled to efficiently minimize stress concentrations in the thin adhesive layer. The unified theory of adhesive-bonded tubular joints was modified one step further to compute the optimum fiber angle variation using the constraint of linear distribution of the axial resultant forces in the adherends. From the methodological viewpoint, the results unveiled that the interfacial shear stress concentration in the adhesive layer was considerably diminished or even vanishes under all loading scenarios. The possibility of multiple optimum composite joints can be achieved, which otherwise are not straightforward to determine when using other analytical tubular joint models and optimization methods. Parametric studies of geometrical variables were also performed to provide a design guideline for optimum coupler joints with efficient mitigation of peak adhesive interfacial stresses.

Topology optimization for the design of a 3D-printed rotating shaft balance

Rotating shaft balances (RSBs) are devices that are used to measure rotor blade forces and moments of wind tunnel models during wind tunnel tests. The design of an RSB can be challenging, because it has to comply with many and sometimes contradicting requirements such as high stiffness and high strain gauge bridge outputs. The manufacturing of a conventional RSB consists of different subsequent steps, which can be time consuming, expensive and associated with many risks. Therefore, in this work, the authors investigate if a RSB can be designed by topology optimization and manufactured by 3D printing. A topology optimization method was developed with as design objective the minimization of strain energy with constraints for the volume of the RSB’s midsection, defined stresses at strain gauge locations used for the measurement of axial force and torque and an overhang constraint for additive manufacturing. The optimal preliminary design found by topology optimization was translated into a final printable design with the highest bridge sensitivity for axial force and torque, sufficient output for in-plane forces and moments and an acceptable safety factor on strength for combined loads. After adding extra supports required for printing, the RSB was successfully printed in metal by the laser powder bed fusion process, resulting in a product without external defects. The same topology optimization and manufacturing method can potentially be used for other balance types, leading to a reduction in total lead time and manufacturing costs while increasing the design freedom.

Smooth Crack Band Model—A Computational Paragon Based on Unorthodox Continuum Homogenization

Abstract The crack band model, which was shown to provide a superior computational representation of fracture of quasibrittle materials (in this journal, May 2022), still suffers from three limitations: (1) The material damage is forced to be uniform across a one-element wide band because of unrestricted strain localization instability; (2) the width of the fracture process zone is fixed as the width of a single element; and (3) cracks inclined to rectangular mesh lines are represented by a rough zig-zag damage band. Presented is a generalization that overcomes all three, by enforcing a variable multi-element width of the crack band front controlled by a material characteristic length l0. This is achieved by introducing a homogenized localization energy density that increases, after a certain threshold, as a function of an invariant of the third-order tensor of second gradient of the displacement vector, called the sprain tensorη, representing (in isotropic materials) the magnitude of its Laplacian (not expressible as a strain-gradient tensor). The continuum free energy density must be augmented by additional sprain energy Φ(l0η), which affects only the postpeak softening damage. In finite element discretization, the localization resistance is effected by applying triplets of self-equilibrated in-plane nodal forces, which follow as partial derivatives of Φ(l0η). The force triplets enforce a variable multi-element crack band width. The damage distribution across the fracture process zone is non-uniform but smoothed. The standard boundary conditions of the finite element method apply. Numerical simulations document that the crack band propagates through regular rectangular meshes with virtually no directional bias.

Enhancement of the behaviour of reinforced concrete dapped end beams including single-pocket loaded by a vertical concentrated force

In precast building construction, some beams are designed to support one or several concentrated loads resulting from the reactions of the attached cross beams. Consequently, the pocket beams without or with dapped ends may represent one of the innovative solutions to constitute the joints between the two attached members. In the present research work, the behaviour of dapped end beams that included rectangular opening loaded with in-plane force, have been investigated. Several detailing have been proposed, in addition the vertical stirrups, to improve the strength of the opening region including the use of steel fibre concrete (SFC),Configuration of the inclined crossed bars, jacketing with steel plates and the composite section technique with two arrangements of the reinforcement of the dapped end . Ten specimens have been tested under gradually increased vertical static loading. The tested specimens are categorized into two sets based on the configuration of dapped end reinforcement. Two variable have been considered which are the strengthening configuration of the opening region and the configuration of the dapped end reinforcement. The response has been discussed in terms several indicators including, the cracking and failure loads, maximum deflection, mode of failure, load-deflection curves, crack patterns, crack width, to recognize the optimum strengthening proposal of the opening. Results revealed that using the inclined steel bars (modified arrangement) yield better response than the conventional (standard) reinforcement (vertical stirrups) within the dapped end. For beams with pockets strengthened with crossed inclined bars, failure load enhanced in range of (8.5-11%) whereas the enhancement was in ranged in (8-10%) for the steel SFC method. Moreover, an improvement by about (11-13%) in load capacity increased when the jacketing with steel plates was applied. The maximum improvement was obtained when using the embedded rolled section within the opening with values of (21-23%).