Bilinear Shape Research Articles

Mechanical characterization of large diameter UHMWPE ropes under quasi-static tensile loading: An experimental study

The Large diameter UHMWPEFR (Ultra High Molecular Weight Polyethylene Fiber Rope) are ideal for heavy lifting and slinging, with their mechanical properties and behaviour characterisation are key to the application.Therefore, this study conducts uniaxial tensile tests on a 115 mm diameter rope (FR-115) to investigate its mechanical properties under quasi-static tensile conditions. considering the anisotropic structural characteristics of UHMWPEFR, a method and criteria for eliminating inter-strand gaps and uneven force through pre-tensioning were proposed. Subsequently, tensile tests were carried out to examine the mechanical properties and constitutive relationship of the rope. The experimental results indicate that pre-tensioning can effectively eliminate the influence of non-elastic deformation of the rope, meeting the formal tensioning requirements based on the stability criteria of the rope structure constructed from mechanical and physical parameters. The stress-strain curve of FR-115 shows a linear bilinear shape without a yield segment during the tensioning process, presenting a typical brittle failure mode. The mechanical behavior is closely related to the historical load effects and loading speed, with the rope transitioning from soft and tough to hard and brittle, exhibiting hysteresis. Based on the above analysis, the graded load and time-varying modulus parameter are fixed, and the internal force is more sensitive to the quasi-static tensile velocity; a two-stage principal model is established based on the analysis of curve characteristics and time-dependent correlation, with 50 % MBS(Minimum Break Strength) as the characterization point, and the UHMWPEFR principal relationship in the pre-period is linear-elastic, and the strain-rate effect is taken into account for the dense section, and the rate correlation and nonlinear characteristics of the dense section of the rope can be accurately portrayed with the introduction of Cowper-Symonds.

Experimental investigation on triaxial mechanical properties of coral coarse aggregate-sea sand seawater concrete

The application of coral coarse aggregate-sea sand seawater concrete (CSSC) in offshore engineering construction is one of the effective measures to realize the rational allocation of resources and alleviate the shortage of resources. In addition, considering that concrete structures in coastal areas may be under triaxial stress, it is necessary to study the triaxial mechanical properties of CSSC. To study the triaxial mechanical properties of CSSC, the effects of aggregate combination and lateral confining pressure on the failure mode, stress-strain curve, yield stress and yield strain of specimens were studied by conventional triaxial tests. The results show that CSSC is more susceptible to the influence of lateral confining pressure. Under the lateral confining pressure of 6 MPa, the crack form transformation and plastic flow appear on the surface of the specimen. Under the lateral confining pressure of 12 MPa, the stress-strain curve appears "stress platform", while the gravel coarse aggregate concrete shows the above changes under the lateral confining pressure of 15 MPa and 24 MPa, respectively. When the lateral confining pressure reaches 15 MPa, the stress-strain curve of CSSC presents a bilinear shape with a second linear branch. With the increase of confining pressure, the damage development rate gradually decreases, and the yield stress and yield strain gradually increase. Finally, the triaxial compression constitutive model of CSSC is established, which can effectively predict the bilinear behavior of the CSSC curve.

Coupled modelling of artificial freezing along clay-sand interface under seepage flow conditions

The artificial freezing in the clay-sand stratum under seepage flow conditions involves the hydro-ice-salt-crystalline-thermal-mechanical coupling process. A theoretical model is derived to investigate the influences of water seepage on the freezing process in the clay-sand stratum. The good agreements between the results from the theoretical model and laboratory tests in the literature verified the accuracy of the proposed model. Parametric studies are conducted to investigate the influences of the seepage velocities and temperature gradients on the spatial distributions. It is found that the ice contents, crystalline salt contents and adsorbed salt contents distribution profiles in the clay-sand stratum are nonlinearly distributed with a cliff distribution curve existing on their interface. The crystalline salt contents in the clay layer are higher than those in the sand layer due to the influence of water seepage and heat transfer. The adsorbed salt contents in the frozen area account for 2% of the total salt contents, but those in the unfrozen area account for 8% of the total salt contents. Due to the volume expansion caused by the soil skeleton deformation, thickness of fractional ice, ice frost heave deformation and salt swelling deformation, the soil deformation distribution curves in the clay-sand stratum are in a bilinear shape.

Quadrilateral element in mixed FEM for analysis of thin shells of revolution

The purpose of study is to develop an algorithm for the analysis of thin shells of revolution based on the hybrid formulation of finite element method in two dimensions using a quadrilateral fragment of the middle surface as a discretization element. Nodal axial forces and moments, as well as components of the nodal displacement vector were selected as unknown variables. The number of unknowns in each node of the four-node discretization element reaches nine: six force variables and three kinematic variables. To obtain the flexibility matrix and the nodal forces vector, a modified Reissner functional was used, in which the total specific work of stresses is represented by the specific work of membrane forces and bending moments of the middle surface on its membrane and bending strains, and the specific additional work is determined by the specific work of membrane forces and bending moments of the middle surface. Bilinear shape functions of local coordinates were used as approximating expressions for both force and displacement unknowns. The dimensions of the flexibility matrix of the four-node discretization element were found to be 36×36. The solution of benchmark problem of analyzing a truncated ellipsoid of revolution loaded with internal pressure showed sufficient accuracy in calculating the strength parameters of the studied shell.

Strain compliance crack model for RC beams: primary versus secondary cracks

This study proposes the Strain Compliance Crack (SCC) model to capture, as reported by tests, the specifics of various cases of crack spacing and width analysis involving primary and secondary cracks in RC beams. The model dwells on calculating crack spacing based on the reinforcement strain profile. As part of the model, a new concept of the limit effective depth, dlim, is proposed to classify crack patterns. When d ≤ dlim (small beam), the pattern consists of primary bending cracks only; when d > dlim (large beam), both primary and secondary cracks are taken into account. Being dependent on the reinforcement ratio, modular ratio, cover, and bar diameter, for most practical cases, dlim ranges from 0.12 to 0.64 m. While the model can predict mean spacing between primary and secondary cracks, only primary cracks are considered for the crack width analysis. A linear crack width profile is assumed for small beams. A bilinear shape (including a fish shape) of the width profile is taken for primary cracks of large beams: between the tips of primary and secondary cracks, width is governed by the primary crack spacing, whereas the remaining part is also affected by the secondary cracks. Crack spacing and width predictions by the proposed model agreed well with the tests.

Behavior of large-scale hybrid FRP–concrete–steel double-skin tubular columns under concentric compression

Hybrid fiber reinforced polymer (FRP)–concrete–steel double-skin tubular columns (hybrid DSTCs) are a novel form of columns with superior load-carrying capacity, ductility, and corrosion resistance. Such columns consist of an outer FRP tube, an inner steel tube, and the concrete filled between the two tubes. While they have attracted extensive research attention worldwide, most of the existing studies have been focused on small-scale specimens. In particular, the behavior of large-scale hybrid DSTCs with a filament-wound FRP tube and self-compacting concrete (SCC) has not been systematically investigated. Against this background, this paper presents a systematic experimental study on large-scale hybrid DSTCs under concentric compression with the following important issues being particularly investigated: the use of large-scale specimens, the use of prefabricated filament-wound FRP tubes compared with wet-layup FRP tubes, and the effect of shrinkage of SCC. The test results confirmed the excellent ductility of hybrid DSTCs and revealed that the types of concrete (SCC versus normal concrete) and FRP tube (wet-layup versus filament-wound tubes) significantly affected the compressive behavior of hybrid DSTCs. Finally, the predictions of an existing design-oriented stress–strain model for confined concrete in hybrid DSTCs, which was developed based on test results of small-scale hybrid DSTCs made with normal concrete and confined with a wet-layup FRP tube, are compared with the test results. It is shown that the model provides reasonably accurate predictions for confined concrete in the large-scale hybrid DSTCs with a typically bilinear shape, but it fails to predict the obvious axial stress drop after the first peak load caused by the large shrinkage of SCC.

Lateral hysteretic behavior of a novel metal rubber bridge bearing

In this paper, a novel metal rubber bearing is proposed as an alternative to the conventional rubber bearings for small- and medium-span highway bridges to solve the aging-related issues of conventional rubber bearings such as chemical degradation and erosion. The bearing is made of porous metal wire by coiling, weaving and cold-pressing to specific shapes. A shear test program is then described on two metal rubber bearings of stainless steel wire with different densities in order to identify the characteristics of hysteretic curves. The effects of shear strain, compressive stress, loading frequency and repeated loading cycles on the hysteretic behavior were investigated. It was found that the lateral hysteretic curves are approximately in bilinear shape, which consists of an initial elastic stage and a post-yield stage. The equivalent damping ratio of the tested bearings was around 20% at 25% shear strain levels and meanwhile increased with the strain levels, indicating an appreciable energy dissipation capacity. In addition, stiffness degradation was observed for the hysteretic curves beyond a certain deformation limit due to the plastic deformation caused by wire delamination and bearing bulging. However, beyond this limit, the bearing could still work as a unit with stable hysteretic behavior. These characteristics make the metal rubber bearing a great candidate for the conventional rubber bearings. It was also found that the hysteretic behavior is related with a variety of parameters such as density, loading frequency and compressive stress. Finally, it was found that the Bouc-Wen model with appropriate input parameters representing the mechanical properties can accurately simulate the hysteretic curves of the proposed bearings.

Adaptive Exponential Finite Elements for a Phase Field Fracture Model

AbstractFracture phenomena can be described by a phase field model in which an independent scalar field variable in addition to the mechanical displacement is considered [3]. This field approximates crack surfaces as a continuous transition zone from a value that indicates intact material to another value that represents the crack. For an accurate approximation of cracks, narrow transition zones resulting in steep gradients of the fracture field are required. This necessitates a high mesh density in finite element simulations, which leads to an increased computational effort. In order to circumvent this problem without forfeiting accuracy, exponential shape functions were introduced in the discretization of the phase field variable, see [4]. These special shape functions allow for a better approximation of steep gradients of the phase field with less elements as compared to standard Lagrange elements. Unfortunately, the orientation of the exponential shape functions is not uniquely determined and needs to be set up in the correct way in order to improve the approximation of smooth cracks. This work solves the issue by adaptively reorientating the exponential shape functions according to the nodal values of the phase field gradient in each element. Furthermore, a local approach is pursued that uses exponential shape function only in the vicinity of the crack, whereas standard bilinear shape function are used away from the crack.

Interfacial failure of circular or tubular hybrid bonded joints: A theoretical description

In different industries, the bonding technique has gained several advances in recent years. However, due to the specificity of each industry, the bonded joints may present different configurations. For instance, in the case of metallic truss bridges, the use of Carbon Fibre Reinforced Polymers (CFRP) bonded on the steel surface members may require circular or even tubular transitions between these materials. Although the bonded transitions between a metal and a composite material have been deeply studied with flat surfaces the information on circular or tubular hybrid bonded joints is still scarce. Therefore, the present study aims to mitigate some of this lack of knowledge by proposing an analytical solution able to describe the interfacial debonding process between a circular or tubular bonded transition between two materials. The proposed model also aims to simulate the interfacial debonding of double butt (or stepped) lap joints. Under these circumstances, a bilinear local adhesive model is adopted which required the quantification of the elastic and the softened stiffnesses as well as the pure Mode II fracture energy. The Finite Element Method (FEM) is used for the validation of the proposed model. The behaviour of the adhesive joint between materials is numerically modelled through the Cohesive Zone Modelling (CZM) in which the same bilinear shape used in the analytical solutions is adopted. Different situations were analyzed thoroughly and the numerical simulations tracked very closely the analytical results obtained from the proposed closed-form solutions.

Topology optimization of natural convection heat transfer using SEMDOT algorithm based on the reduced-order model

Due to the strong nonlinear nature and the mutual effect between the temperature field and the velocity field, it is very difficult to solve the natural convection heat transfer problem. To this end, the Gauss Seidel iterative algorithm based on the reduced-order model is proposed to decouple temperature and pressure. In this paper, the governing equations are discretized by finite element method using bilinear shape functions. To suppress the oscillation of the solution of the governing equations, Streamline Upwind Petrov-Galerkin method (SUPG) is adopted. The main idea of the Gauss Seidel iterative algorithm is: given an initial temperature, pressure and temperature are obtained successively by solving only two nonlinear equations, which greatly improves the computational efficiency. Compared with full order Navier-Stokes model, the Gauss Seidel iterative algorithm for reduced order model has similar results. Then, in order to generate accurate boundaries, Smooth-Edged Material Distribution for Optimizing Topology (SEMDOT) based on density method (SIMP) is studied. Finally, some numerical examples demonstrate the feasibility and effectiveness of the proposed scheme.

A novel mixed finite element formulation based on the refined zigzag theory for the stress analysis of laminated composite plates

This study presents an accurate mixed variational formulation for the stress analysis of laminated composite plates based on Refined Zigzag Theory (RZT). A two-field variational concept based on the Hellinger-Reissner (HR) principle is employed associated with the kinematic assumptions of the RZT. The RZT provides a good mixture between the accuracy and computational efficiency for the thin and thick laminated composite structures without using the shear correction factors. A four-noded quadrilateral element and bi-linear shape functions are used for the discretization of the solution domain ensuring the C0-continuity. The main novelty of the present study is that the flexural behavior of the laminated composite plates is investigated based on RZT within the light of HR principle using monolithic approach for the first time. The proposed Mixed Finite Element (MFE) formulation assigns stress resultant type field variables in addition to the kinematic variables of the RZT. Therefore, the present approach, MRZT, paves the way of obtaining the stress resultants at each node directly from the solution of the system equations. Since the shear forces are obtained at each node, Equivalent (transformed) Section Principle (ESP) is utilized to achieve continuous through thickness transverse shear stress variations. In-plane strain components are calculated through the compliance matrix without resorting to the spatial derivatives of displacement components. The robustness and capability of the present approach are established through benchmark problems, and its applicability to challenging problems is demonstrated by modeling thick and highly heterogeneous plates, a delaminated plate and three-point bending tests.

Static and free vibration analysis of thin arbitrary-shaped triangular plates under various boundary and internal supports

Thin triangular plate is one of the common structural members widely used in engineering structures. A weak form numerical method is presented for the static and free vibration analysis of thin arbitrary-shaped triangular plates under various boundary and internal supports. With the help of the sub-parametric technique, the triangular plate domain is first mapped into a regular one with bilinear shape functions and then the discretization is carried out in the regular domain. Gauss quadrature is used to avoid zero of Jacobian determinant at a plate corner. Explicit formulas are worked out for an arbitrary number of nodes. A number of numerical examples are studies. Comparisons show that the presented method is simple and highly accurate. Thus the method may also be used in the design stage for the optimization design of plate shapes as well as lamination sequences of laminated plates.

Adaptive numerical integration of exponential finite elements for a phase field fracture model

Phase field models for fracture are energy-based and employ a continuous field variable, the phase field, to indicate cracks. The width of the transition zone of this field variable between damaged and intact regions is controlled by a regularization parameter. Narrow transition zones are required for a good approximation of the fracture energy which involves steep gradients of the phase field. This demands a high mesh density in finite element simulations if 4-node elements with standard bilinear shape functions are used. In order to improve the quality of the results with coarser meshes, exponential shape functions derived from the analytic solution of the 1D model are introduced for the discretization of the phase field variable. Compared to the bilinear shape functions these special shape functions allow for a better approximation of the fracture field. Unfortunately, lower-order Gauss-Legendre quadrature schemes, which are sufficiently accurate for the integration of bilinear shape functions, are not sufficient for an accurate integration of the exponential shape functions. Therefore in this work, the numerical accuracy of higher-order Gauss-Legendre formulas and a double exponential formula for numerical integration is analyzed.

Adaptive Orientation of Exponential Finite Elements for a Phase Field Fracture Model

AbstractOne technique to describe the failure of mechanical structures is a phase field model for fracture. Phase field models for fracture consider an independent scalar field variable in addition to the mechanical displacement [1]. The phase field ansatz approximates crack surfaces as a continuous transition zone in which the phase field variable varies from a value that indicates intact material to another value that represents cracks. For a good approximation of cracks, these transition zones are required to be narrow, which leads to steep gradients in the fracture field. As a consequence, the required mesh density in a finite element simulation and thus the computational effort increases. In order to circumvent this efficiency problem, exponential shape functions were introduced in the discretization of the phase field variable, see [2]. Compared to the bilinear shape functions these special shape functions allow for a better approximation of the steep transition with less elements. Unfortunately, the exponential shape functions are not symmetric, which requires a certain orientation of elements relative to the crack surfaces. This adaptation is not uniquely determined and needs to be set up in the correct way in order to improve the approximation of smooth cracks. The issue is solved in this work by reorientating the exponential shape functions according to the nodal value of phase field gradient in a particular element. To be precise, this work discusses an adaptive algorithm that implements such a reorientation for 2d and 3d situations.

On static and free vibration analysis of FGM plates using an efficient quadrilateral finite element based on DSPM

In the present paper, a shear-locking free quadrilateral element with 5 DOFs per node, called Q4γs, is developed using a discrete shear projection method (DSPM). Independent transverse shear strains are formulated using a tangential coordinate system, and discrete shear strains are applied along each of element sides to get the constant shear strains. These constant independent transverse shear strains are projected onto each corner node, and the cartesian shear strain components are interpolated over the element domain with standard bilinear shape functions. The applications of the element in static and free vibration analysis of functionally graded material plates show good convergence behavior, high reliability, and accuracy.

Effects of the progressive damage interphase on the effective bulk behavior of spherical particulate composites

This work aims at investigating the effect of the progressive damage interphase on the global bulk behavior of spherical particulate composites by proposing a nonlinear stress-strain relationship. To this end, first, the modeling of a damage interphase as a damage imperfect interface is briefly presented in a mathematically rigorous manner. The relationship between the proposed interface model and the classical cohesive model is also discussed and depicted by taking the example of the bilinear shape cohesive model. Second, the elastic fields of the problem where an infinite body made of a matrix containing a spherical particle with a damage interface under a remote uniform isotropic strain boundary condition are then provided in the framework of a Cartesian coordinate system, and the critical macroscopic strain boundary associated to the initial softening of the damage interface is determined. Third, with the aid of these results, the equivalent elastic properties of a perfectly bonded spherical particle related to an imperfectly damage bonded one in an infinite matrix are derived by the replacement procedure of equivalent inclusion with the requirement of energy equality. Finally, the effective bulk of the isotropic particulate composite is obtained by using the classical generalized self-consistent scheme; its global strength is also given, and their features are discussed through some numerical examples.

The strain-smoothed 4-node quadrilateral finite element

Recently, the strain-smoothed element (SSE) method has been developed for 3-node triangular and 4-node tetrahedral solid elements. The method was also applied for enhancing the membrane performance of a 3-node triangular shell element (MITC3+ element). Using the SSE method, convergence behaviors of the finite elements were significantly improved without additional degrees of freedom. However, the application of the SSE method is limited to constant strain finite elements such as 3-node triangular and 4-node tetrahedral elements. In this paper, the SSE method is applied to a 4-node quadrilateral finite element. Doing so, the piecewise linear shape functions are employed instead of standard bilinear shape functions. The proposed strain-smoothed 4-node quadrilateral element passes all the basic tests, and shows a significantly improved accuracy in various numerical examples.

Axial compressive behavior and confinement mechanism of circular FRP-steel tubed concrete stub columns

Fiber-reinforced polymer (FRP)-steel tubed concrete (FSTC) columns have emerged as a new type of compression members. An experimental program was performed to further demonstrate the axial compressive behavior of FSTC stub columns and to clarify the confinement mechanism in such members. The test results showed that the capacities of the axially loaded FSTC specimens were enhanced with the increase of the FRP confinement and the decrease of the steel tube’s diameter-to-thickness (D/t) ratio. After deducting the steel tube’s axial bearing contribution through elastic–plastic analysis, the concrete cores’ axial load–strain responses had a bilinear shape, which was very similar to the axial load–strain responses of the composite columns. Based on the comparison between steel confinement and FRP confinement, a confinement mechanism was proposed to reveal the interaction between the inner concrete core and the outer FRP-steel composite tube. It was divided into three stages: domination of steel confinement, domination of FRP-steel dual confinement, and domination of FRP confinement. The total confining pressure at the third stage could be considered as a translational motion of the FRP confining pressure, which explained why the second stiffness of the confined concrete was more sensitive to the FRP confinement stiffness than the steel confinement.

New finite element model for the stability analysis of a functionally graded material thin plate under compressive loadings

The main objective of this work is to present a finite element model for the stability analysis of functionally graded material thin plates subjected to uniaxial and biaxial loads. This model is developed using the classic thin plate’s kinematics of von Karman. Static equilibrium equations are established by means of the principle of stationary potential energy. The formulation is made without any homogenization technique or rule of mixtures; thus, the stress and strain vectors are split into two parts: a membrane part and a second bending part. For the elastic behavior matrix, it is written in dimensionless form. The finite element discretization is done using a four-node quadrilateral element with five degrees of freedom per node. Lagrange bilinear shape function are adopted for the membrane components, and Hermite’s high-degree shape function are adopted for the flexural component. The critical buckling loads are established by solving the eigenvalue problem. The efficiency of the model is tested on several examples of buckling plates under different types of loading. In the present study, specimens of rectangular and perforated plates were tested in three different loading conditions: uniaxial compression, biaxial compression, and compression–traction.

Volume change behavior of saturated compacted GMZ bentonite and slurry during cyclic loading-unloading processes

In order to investigate the volume change behavior of saturated GMZ bentonite during cyclic loading-unloading processes, oedometer tests with cyclic loading-unloading process were conducted on saturated compacted GMZ bentonite and slurry specimens. A significant hysteretic loop was observed in compression curve of saturated compacted GMZ bentonite during cyclic loading-unloading process. Compression curve of the slurry specimen presented a bilinear shape. Under smaller stresses (<0.5~2MPa), the unloading-reloading loop was insignificant. However, under higher stresses (>0.5~2MPa), the unloading-reloading loop was significant. The unloading-reloading loop could be explained by the competition between the mechanical and physico-chemical effects on the microstructure changes. When stress was higher than 10MPa, compression curve of the slurry gradually closed to and coincided with the compression curve of the compacted bentonite specimen. Therefore, normal consolidation line of GMZ bentonite could be determined based on the overlapped part of the compression curves.