Bending Stiffness Parameters Research Articles

Learning-Based Bending Stiffness Parameter Estimation by a Drape Tester

Real-world fabrics often possess complicated nonlinear, anisotropic bending stiffness properties. Measuring the physical parameters of such properties for physics-based simulation is difficult yet unnecessary, due to the persistent existence of numerical errors in simulation technology. In this work, we propose to adopt a simulation-in-the-loop strategy: instead of measuring the physical parameters, we estimate the simulation parameters to minimize the discrepancy between reality and simulation. This strategy offers good flexibility in test setups, but the associated optimization problem is computationally expensive to solve by numerical methods. Our solution is to train a regression-based neural network for inferring bending stiffness parameters, directly from drape features captured in the real world. Specifically, we choose the Cusick drape test method and treat multiple-view depth images as the feature vector. To effectively and efficiently train our network, we develop a highly expressive and physically validated bending stiffness model, and we use the traditional cantilever test to collect the parameters of this model for 618 real-world fabrics. Given the whole parameter data set, we then construct a parameter subspace, generate new samples within the sub-space, and finally simulate and augment synthetic data for training purposes. The experiment shows that our trained system can replace cantilever tests for quick, reliable and effective estimation of simulation-ready parameters. Thanks to the use of the system, our simulator can now faithfully simulate bending effects comparable to those in the real world.

Learning Physics Property Parameters of Fabrics and Garments With a Physics Similarity Neural Network

Predicting the physics properties of deformable objects such as garments and fabrics is a challenge in robotic research. Directly measuring their physics properties in a real environment is difficult [1]. Therefore, learning and predicting the physics property parameters of garments and fabrics can be conducted in simulated environments. However, garments have collars, sleeves, pockets and buttons that change the way garments deform and simulating these is time-consuming. Therefore, in this paper, we propose to predict the physics parameters of real fabrics and garments by learning the physics similarities between simulated fabrics via a Physics Similarity Network (PhySNet). For this, we estimate wind speeds generated by an electric fan and area weights to predict the bending stiffness parameters of real fabrics and garments. We found that PhySNet coupled with a Bayesian optimiser can predict physics property parameters and improve state-of-art by 34.0% for fabrics and 68.1% for garments.

Buckling optimization of composite rectangular plates by sequential permutation search with bending-twisting correction

Buckling problem of composite plates is of importance since it is commonly encountered in thin-walled structural components in engineering. Buckling resistance design of composite plates involves the design of laminate stacking sequence exhibiting high dimensional discrete variables owing to the combination and permutation of ply orientations of layers. In this work, a sequential permutation search (SPS) optimization algorithm is presented for the stacking sequence design of composite rectangular plates accounting for the inherent physical-mechanical behavior of composite laminates. Owing to that the governing equation for buckling of composite rectangular plates is a linear homogeneous equation on bending stiffness parameters, the convexity of flexural lamination parameters and sensitivity of bending stiffness are utilized to construct sensitive detection techniques and linear search procedures. Moreover, to increase the robustness of SPS, a sign optimization algorithm (SOA) is coupled in SPS to regulate bending-twisting coupling effects. The SPS algorithm is applied to the buckling resistance design of composite rectangular plates exhibiting various boundaries under axial compression, where the Rayleigh-Ritz method is developed to perform the buckling analysis. Optimal results of SPS are compared against layerwise optimization approach (LOA) and genetic algorithm (GA), illustrating its reliability and efficiency.

Simulating the effect of fabric bending stiffness on the wrinkling behaviour of biaxial fabrics during preforming

A macroscopic finite element model has been established to investigate the forming-induced wrinkling behaviour for bi-axial fabrics. Results indicate that using a linear bending model with a constant bending stiffness produces unrealistic wrinkle patterns in the fabric plies. A non-linear bending model produces more accurate forming induced wrinkle patterns compared to experimental data, since the bending stiffness parameter is varied as a function of the applied forming load to account for the onset of fibre buckling. Areas of high in-plane shear are more likely to induce out-of-plane wrinkles, indicating a positive correlation between wrinkling onset and shear deformation. A new methodology has been developed to quantitatively evaluate the severity of fabric wrinkles based on the FE simulation results. The distance between the surface of the preform and the mould tool is used to locate areas with out-of-plane defects, using the principal curvature to isolate wrinkles from areas of fabric bridging (poor conformity).

An analytical investigation on the new design of 3-DOF flexible nanopositioner driven by electrostatic actuators

With the increasing development of nanopositioning stages, the study of their deformation and instability under various actuators is very important. Accordingly, in the present paper, the nanopositioning mechanism based on flexible links with the ability to move in three directions of XYZ is introduced using an electrostatic actuator. Then, using the analytical method, static behavior and performance of this mechanism under the influence of electrostatic force are studied. For this purpose, part of this mechanism, which includes a flexible beam with the electrostatic force, is considered. Then, using the nonlinear Euler–Bernoulli beam theory and taking into account the nonlinear effects arising from the radius of curvature, for the first time, the nonlinear differential equation is extracted. Applying the step-by-step linearization method and assuming the static voltage applied to the end of the flexible beam, the effect of different parameters on static deformation is investigated. The results of this study show that considering the nonlinear effects caused by curvature radius has a significant effect on the mechanical behavior of the system, and with increasing the value of this parameter, the hardening behavior of the flexing beam increases. This reduces the static deflection of the flexible beam in comparison with the results of linear theory. Also, by increasing the voltage applied to the flexible beam, the created nonlinear strains are increased, and the nonlinear effects of the radius of curvature become significant. For example, with an increase in the dimensionless bending stiffness parameter from 0 to 10 × 10−3, the maximum deflection of the flexible beam for 10 V, 15 V, and 20 V voltages decreases by 7.7%, 35.8%, and 48.6%, respectively.

Spherical nano-inhomogeneity with the Steigmann–Ogden interface model under general uniform far-field stress loading

An explicit solution, considering the interface bending resistance as described by the Steigmann–Ogden interface model, is derived for the problem of a spherical nano-inhomogeneity (nanoscale void/inclusion) embedded in an infinite linear-elastic matrix under a general uniform far-field-stress (including tensile and shear stresses). The Papkovich-Neuber (P-N) general solutions, which are expressed in terms of spherical harmonics, are used to derive the analytical solution. A superposition technique is used to overcome the mathematical complexity brought on by the assumed interfacial residual stress in the Steigmann-Ogden interface model. Numerical examples show that the stress field, considering the interface bending resistance as with the Steigmann–Ogden interface model, differs significantly from that considering only the interface stretching resistance as with the Gurtin–Murdoch interface model. In addition to the size-dependency, another interesting phenomenon is observed: some stress components are invariant to interface bending stiffness parameters along a certain circle in the inclusion/matrix. Moreover, a characteristic line for the interface bending stiffness parameters is presented, near which the stress concentration becomes quite severe. Finally, the derived analytical solution with the Steigmann–Ogden interface model is provided in the supplemental MATLAB code, which can be easily executed, and used as a benchmark for semi-analytical solutions and numerical solutions in future studies.

Behavior of concrete beams reinforced with GFRP under transverse force

The article discusses the effect of transverse reinforcement spacing for the strength and deformation characteristics of beams with glass fibre reinforced polymer. The bending tests results of reinforced concrete specimens are presented (GFRP) with different concrete strength and reinforcement spacing. Force-deflection, force-GFRP bars deformation and force-concrete compressed zone deformation dependencies are given in the article. Based on ultimate force and beams destruction pattern it is established that increasing transverse reinforcement spacing reduces the beams strength and leads to destruction in oblique section. With narrow-mashed transverse reinforcement fracture occurs in the compressed zone of concrete. A computational analysis for different types of beams fracture is presented. It is established that transverse reinforcement spacing doesn’t affect the parameters determined by service limit state: crack formation load, crack width and beam deflection. A comparative analysis of maximum permissible deflection based on test results and theoretical calculations was carried out. The numerical values of bending stiffness parameter are obtained at the loading stages with linear deformation before and after first crack formation.

On the Elastic Plates and Shells with Residual Surface Stresses

Recently the interest grows to development of the theory of surface elasticity with respect to nanotechnologies. Nanostructured materials demonstrate very promising properties which are different from whose of bulk materials, in general. In particular, nanosized specimens exhibit size-effect that is dependence of apparent (effective) material properties such as Young's modulus on specimen's size. One of possible explanation of these phenomena is the consideration of surface-related phenomena and their influence on the effective properties at the macroscale. In fact, surface elasticity may dramatically change effective (apparent) properties of nano- and microstructure materials.We discuss here the effective properties of thin-walled structures that are tangential and bending stiffness parameters taking into account surface/interfacial initial stresses. We consider the Gurtin-Murdoch model of surface elasticity. We show that the surface elasticity results in positive size-effect that is stiffening of nano-sized bodies in comparison with their bulk counterparts. Special attention will be paid to residual surface stresses. Unlike to surface elastic moduli there are no restrictions for values of residual stresses. In particular, we show that the compressive residual stresses may lead to negative size-effect that is to decreasing of an effective stiffness for nano-sized specimens.

A simplified elastic analysis of tunnel-piled structure interaction

In urban areas, engineers often need to assess tunnelling-induced displacements of piled structures and the resulting potential for damage. This paper presents an elastic study of tunnel-pile-structure interaction through Winkler-based Two-Stage Analysis Methods (TSAMs), focusing on structural displacements resulting from tunnel excavation beneath piled frames or simple equivalent beams. Comparison of results with 3D finite element analyses shows that the simple TSAM models are able to provide a good assessment of tunnelling-induced building displacements. Parametric analyses highlight the role of tunnel-pile interaction and the superstructure (stiffness, configuration, and pile-structure connections) in the global response of the tunnel-soil-building system. In particular, the effect that key parameters have on deflection ratios and horizontal strains are investigated. Results illustrate how piled foundations increase the risk of structural damage compared to shallow foundations, whereas structural stiffness can reduce building deformations. Flexural deformations are predominately induced by tunnel excavations beneath piles whereas horizontal strains at the ground level are negligible when a continuous foundation is included. Furthermore, it is illustrated that results based on buildings modelled as equivalent beams can differ considerably compared to when they are modelled as framed structures. Simple design charts are provided to estimate horizontal strains and deflection ratio modification factors based on newly defined relative axial and bending stiffness parameters which account for the presence of the piles.

Method of Bending Stiffness Parameter Identification of Stay Cable

In order to solve the problem of bending stiffness parameters identification of practical stay-cable, and provide bending stiffness correction for tension measurement. A method to identify cable bending stiffness parameters is proposed, and its basis theory established in paper. The method was applied to Xiazhang Sea-Crossing Bridge, the results showed that: Identification bending stiffness ratio is between 0.33 to 0.54 for relatively short cables of South Branch Bridge, and it tends to decrease with increase of cable length and force. However, the identification bending stiffness is close or equal to 0 EImax for relatively long cable of North Branch Bridge. It testified that the effect of bending stiffness for long cable tension is small in engineering.

Analytical Method for Plate Theory-Based Calculation of Bridge Transverse Load Distribution Coefficient

The most widely used calculation method for bridge transverse distribution coefficient based on plate theory is G-M method. The twisted parameter and bending stiffness parameter are firstly obtained in its calculation process, the distribution coefficient can be determined through inquiring the tables established by Guyon and Massonnet. The work for this computation is huge and the errors are inevitably exist in the stage of inquiring tables. Therefore, an analytical method is proposed in this paper, the partial differential equations of deflection surface can be acquired through analysis and corresponding calculating program is prepared. Numerical simulation of simply supported bridge is presented for validating its feasibility.

Exact dynamic analysis of composite beams with partial interaction

The partial differential equations and general solutions for the deflection and internal actions and the pertaining consistent boundary conditions are presented for composite Euler–Bernoulli members with interlayer slip subjected to general dynamic loading. Both free and forced vibrations are treated. The solutions are shown to be unique and complete under certain conditions, and valid for all so-called restricted admissible boundary conditions. Specifically, the exact eigenmode length coefficients are derived for the four Euler BC. They differ from those valid for ordinary, fully composite (solid) beams, except for the pinned–pinned case. The maximum deviation for beams with the other three Euler BC is shown to be less than 2–6% with respect to the eigenmode length coefficient and 3–10% with respect to the eigenfrequency, respectively, depending on the two non-dimensional parameters, composite action or shear connector stiffness and relative bending stiffness parameters. However, these deviations occur in a rather narrow range of the determining parameters, so for most practical cases the eigenmode length coefficients given for solid (fully composite) beams can approximately be used also for partially composite beams. The procedures of analysing beam vibrations are applied to a specific case. These solutions illustrate the effect of interlayer connection on the peak velocity of the beam vibrations. The proposed analytical theory is verified by tests and finite element calculations.

A simplified analysis method for composite beams with interlayer slip

A simplified static procedure is proposed for analysing and designing composite beams with interlayer slip. The method is parallel to the Eurocode 5 method, but it is general in nature and can be applied to arbitrary boundary and loading conditions. In contrast with Eurocode 5, a general and correct way of choosing the effective beam length of the problem is given by the present procedure, which is that the effective beam length equals the buckling length that is found in the corresponding column buckling problem. The procedure predicts the deflections and internal actions and stresses, in principle by replacing the fully composite bending stiffness ( EI ∞) with the effective (partially) composite bending stiffness ( EI eff) in the expressions for these quantities in the corresponding fully composite beam. This effective bending stiffness depends on two non-dimensional parameters: the composite action parameter (shear connection stiffness) and the relative bending stiffness parameter. The method is applied to a number of simple practical cases and the results obtained have been compared with the exact values. The applicability of the simplified analysis procedure was found to be very good, except for interlayer shear stresses. The error in the Eurocode 5 procedure, as compared with the method proposed in this paper, can in some cases be up to almost 30% depending on the boundary conditions.

Exact static analysis of partially composite beams and beam-columns

The ordinary differential equations and general solutions for the deflection and internal actions and, especially, the pertaining consistent boundary conditions for partially composite Euler–Bernoulli beams and beam-columns are presented. Static loading conditions, including transverse and axial loading and first- and second-order analyses are considered. The theoretical procedure is applicable to general loading and boundary conditions for uniform composite beams and beam-columns with interlayer slip. Further, the exact closed form characteristic equations and their associated exact buckling length coefficients for composite columns with interlayer slip are derived for the four Euler boundary conditions. It is shown that these coefficients are the same as those for ordinary fully composite (solid) columns, except for the Euler clamped-pinned case. For the clamped-pinned case, the difference between the exact buckling length coefficient and the corresponding value for solid columns is less than 1.8% depending on the so-called composite action parameter and relative bending stiffness parameter. Correspondingly, the maximum deviation between the exact and approximate buckling load is at most 2.5%. These small differences can in most practical cases be neglected. Also, the maximum theoretical range for the relative bending stiffness for partially composite beams and beam-columns is derived. An effective bending stiffness, valuable in the determination of the critical buckling load for partially composite members, is derived. This effective bending stiffness is also suitable for analysing approximate deflections and internal actions or stresses in composite beams with flexible shear connection. The beam-column analysis is applied to a specific case. The difference in the approaches to the first- and second-order analysis is illustrated and the results clearly show the magnification in the actions and displacements due to the second-order effect. The magnification of the internal axial forces is different from magnifications obtained for the other internal actions, since only that portion of an internal axial force that is induced by bending is magnified by the second-order effect.

Numerical investigation of the modal sensitivity of suspended cables with localized damage

This paper examines the effect of damage location and size on the modal sensitivity of suspended cables. A numerical finite difference approach that takes account of sag-extensibility and bending stiffness is programmed and adapted to investigate the modal behaviour of suspended cables with induced damage. The finite difference program developed is used to conduct an extensive parametric study on 12 cables with different combinations of sag-extensibility and bending stiffness parameters. A systematic study of the dynamic behaviour of the cables under various damage cases is carried out and original findings are thoroughly discussed. It is shown that despite the complexity of the relationship between damage and the dynamic properties of the cables, definite trends could be identified, especially for out-of-plane vibrations.

Soil Arching over Deeply Buried Thermoplastic Pipe

Soil arching associated with buried thermoplastic pipe is discussed. First, the soil arching phenomenon is described. Then two different approaches are mentioned from the literature to represent the degree of soil arching (or vertical arching factor). The elastic solutions of Burns and Richard are revisited to derive expressions for the vertical soil arching factor for buried pipe. Comparison of the elastic solutions and field soil pressure cell readings reveals the importance of incorporating a bending stiffness parameter. With this finding, the AASHTO method for calculating the load on buried pipe is evaluated against the elastic solutions. The analysis reveals that the AASHTO method is conservative, overestimating the load on thermoplastic pipe by up to 30%. Further evidence to support the finding is found within the strain gauge readings taken on the pipe walls in the field. Therefore, alternative equations derived directly from the elastic solutions are recommended to predict the load on buried thermoplastic pipe instead of the AASHTO method.

The use of generalized functions in the problem of elastic oscillations of a composite rod

The motion of a multicomponent anthropomorphic model is described by the equation of degenerate transverse oscillations of a one-dimensional system of rods with distributed mass and bending stiffness parameters and with concentrated inclusions into these parameters. The concentrated inclusions can be introduced into the analytic expression for the distributed parameters using impulse functions of the first and higher orders (the delta-function and its derivatives). The solution of the equation is found by the operational method. Krylov's generalized functions make it possible to obtain an analytic solution of the equation, which can be realized on a computer, and is written for the whole multicomponent structure at once in the framework of the direct and inverse problems of mechanics. Some optimization problems for a model of the motion of a sportsman are solved in the framework of the direct problem of mechanics.