Cross-sectional Deformation Research Articles

Data-driven approach for a one-dimensional thin-walled beam analysis

This study presents a data-driven approach for developing a one-dimensional thin-walled beam model. In order to analyze complicated deformations occurring in a thin-walled beam by a beam theory, it is important to identify core cross-sectional deformations that are the bases for the one-dimensional beam analysis. In this study, we derive core cross-sectional deformations through data processing using the shell-based static analysis results of a thin-walled beam. We perform a principal component analysis for the data processing, in which the desired core cross-sectional deformations are obtained without specific assumptions pertaining to the behavior of the beam’s sectional deformations. Then, the core cross-sectional deformations can be obtained in explicit functional forms (shape functions) to facilitate the subsequent one-dimensional higher-order beam analysis. Important issues related to the establishment of a well-defined dataset are addressed. Using the data-driven shape functions, a series of static, vibration and buckling analyses are performed for various thin-walled beams. We demonstrate by numerical examples that the present data-driven results agree well with those obtained by shell analysis results. While the shape functions are obtained only from the static analysis results, the vibration and buckling analyses using them were also found to be sufficiently accurate.

Observe the temporal evolution of deep tunnel's 3D deformation by 3D laser scanning in the Jinchuan No. 2 Mine

The three-dimensional (3D) deformation of underground tunnel is meaningful for assessing its mechanical stability, especially for the tunnel with large deformation disaster. In this study, a technology for measuring the 3D deformation of tunnel is presented based on a 3D laser scanner and processing algorithm for point cloud data. This technology includes splicing technology for multi piece point clouds in the same time, filtering technology for 3D point cloud data at individual times, alignment technology for point cloud data from different times, and data extraction technology for typical cross-section deformation of the tunnel and calculates the 3D deformation of the tunnel at different times. This technology was applied to monitor the temporal evolution of the 3D deformation of a deep tunnel in the Jinchuan No. 2 Mine, where the large deformation of the surrounding rock caused serious failure of the supporting structures. The resulting characterization of the dimensional and temporal deformation process of the surrounding rock in the Jinchuan underground tunnel included the 2D deformation distribution characteristics of the cross section, the spatial deformation distribution of the tunnel’s 3D surface, and the 4D spatiotemporal evolution process of the tunnel’s deformation. The observed results provide key information for predicting deformational performance and determining the reasonable support opportunity for a tunnel undergoing large deformation problem.

Prediction of liquid jet trajectory in supersonic crossflow and continuous liquid column model

The trajectory of the spray is studied theoretically and experimentally when a round liquid jet is injected into a supersonic crossflow vertically. A solid model of continuous liquid column is established in three-dimensional space. The cross-section deformation equation of the continuous liquid column along the injection direction is established using a method of micro-element analysis. The stress analysis of cross section is simplified into a two-dimensional droplet. The shape of the cross section is considered to continuously change from circular to elliptical shape. And the bow shock wave in front of the jet column is simplified into an oblique shock wave with a known shock angle. Based on this, the calculation of aerodynamic force is greatly simplified. A dimensionless parameter named effective deformation time of liquid column (the logogram is <inline-formula><tex-math id="M300">\begin{document}${t_{\rm valid}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200903_M300.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="23-20200903_M300.png"/></alternatives></inline-formula>) is defined and used to judge the end point of the liquid column quantitatively. The liquid jet trajectory and cross-section deformation can be calculated using MATLAB software. The instantaneous images of continuous liquid columns in supersonic crossflow are captured using high-spatial-resolution microscopic imaging methods. The microscopic imaging system is composed of a double pulse solid-state laser, computer, CCD camera, synchronous controller, microscope lens and laser diffuser. After passing through the laser diffuser, a plane background light with uniform distribution is formed on the scattering plate. The mean filtering method is used to filter the original image. After filtering, the range of gray distribution in the background area is obviously reduced. The distribution of gray value is more concentrated, and the background of the image is more uniform. Then the image edge detection function is used to obtain the near-field jet trajectory. The parameter variables studied include liquid injection pressure drop (1–2 MPa), liquid nozzle diameter (0.5 mm/1.0 mm), and liquid gas momentum ratio (3.32–7.27). The results show that the continuous liquid column model can better predict the jet trajectory on the center plane and the shape of the liquid column in three-dimensional space. It is indicated that the predictive result matches well with the experimental result. This study is of great significance for establishing the solid-particle coupling model of liquid jet in supersonic crossflows.

Nonlinear Response of a Subsea Tunnel Constructed by Two Tunnelling Methods subjected to Strong Seismic Shaking

In this paper, a three-dimensional numerical model is built to study the seismic response of a subsea tunnel constructed by two tunnelling methods, including the TBM tunneling and drill-and-blast tunneling. In the numerical model, the plastic-damage model is used to simulate the elastic and plastic behaviour of concrete under dynamic loadings. To illustrate the seismic response of the tunnel and yet limit the amount of data included in the paper, the work presented is limited to the deformation of tunnel cross sections and dynamic stress responses. Based on the results, the deformation and stressed of different tunnel sections are discussed. Results show that the amplitude of maximal principal stress occurs at sidewall basement of the inner liner. The spandrel and the sidewall basement are the most precarious area.

Ultrasonic guided wave detection of U-shaped pipeline

The guided waves in the elbow was analyzed using semi- analytical finite element method, which was used to calculate the dispersion curves, along with the vibration deformation and energy flow density distribution of the elbow cross-section. The L(0,1) mode guided wave was used to detect different defects in the U-shaped pipeline in experiment. The average experimental velocity of L(0,1) mode in U-shaped pipeline was between the theoretical velocities of the straight pipe and the elbow, due to the different velocities in the two parts. The detection sensitivity difference of L(0,1) mode guided wave to defects in intrados and extrados of the elbow was analyzed, the experimental result showed that the reflected signal amplitude of defect in extrados was significantly larger than the defect in intrados, which was consistent with the energy flow density distribution in elbow cross-section.

Selection criterion of material filling in ridge grooves for reducing cross-sectional deformation of double-ridged rectangular bent tube

In order to satisfy the further improvement of new communication equipment, filling the ridge grooves on side walls with fillers is the effective method to improve the quality of double-ridged rectangular bent tube in H-typed rotary draw bending. However, how to choose appropriate material filling in ridge grooves to reduce deformation more effectively is a critical issue. Therefore based on the reliable FE models of H-typed rotary draw bending and twice-springback of double-ridged rectangular tube with fillers with different material parameters, a selection criterion of the material of filler to minimize the cross-sectional deformation of bent tube was studied. The selection criterion is that only the height size accuracy of filler should be made sure to be consistent with that of the ridge groove. The strength coefficient K of filler should be considered firstly, and the larger K can reduce the deformation more effectively. The yield strength σs and hardening exponent n can be considered secondly, and filler with higher σs or smaller n can be selected as far as possible. Elastic modulus E may not be taken into account. The reliability of this selection criterion is verified by using 65Mn spring steel filler.

Computed Tomography-based Patient-specific Biomechanical and Fluid Dynamic Study of Anomalous Coronary Arteries with Origin from the Opposite Sinus and Intramural Course.

The anomalous coronary arteries originating from the opposite sinus of Valsalva (ACAOS) constitutes one of the most clinically relevant coronary artery anomalies in adults. Exact pathophysiology and the impact of intramural (IM) course segment stenting in ACAOS with IM course (ACAOS-IM) has not been clarified. We aimed to elucidate the pathophysiology and impact of stenting applying biomechanical and computational fluid dynamics to computed tomography (CT) in patient-specific coronary vessel reconstruction. We separated coronary artery (left or L-, right or R-) ACAOS-IM into segments (proximal, mid and distal), based on coronary angiography and coronary CT angiography features, in a series of patients at Rovigo General Hospital, Italy, between 1 January 2003 and 1 January 2018. Blood pressure gradient across the coronary circulation, calculated blood flow, vorticity magnitude, wall shear stress (WSS) and IM segment deformation were analysed by simulating exercise, before and after virtual stent implantation. In 21 symptomatic patients (13 males, mean age 46.1 ± 8.1 years, L-ACAOS-IM in 9 and R-ACAOS-IM in 12 patients), computational fluid dynamic analysis in both L- and R-ACAOS demonstrated higher basal WSS values in the IM course (9.5 ± 0.2 and 8.6 ± 0.2 Pa for R- and L-ACAOS, respectively), than in the rest of the vessels. These values decreased after stenting. Vorticity magnitude significantly decreased after stenting as well, compared with baseline. Biomechanical deformation analysis revealed not only compression, but also a twisting of the IM segment with a mean distal pressure drop of 32% and 35% in R- and L-ACAOS, respectively, which was corrected by stent implantation. In both L- and R-ACAOS subtypes, the IM segment appeared to be phasically compressed and deformed with a degree of twisting that causes resting and exercise cross-sectional deformation and a drop in distal pressure. Stenting of the IM segment results in normalisation of the flow profile, correction of the IM segment deformation and reverses the drop in pressure, for both variants of ACAOS.

Effect of large displacements on the linearized vibration of composite beams

Natural frequencies and mode shapes are functions of the equilibrium state. In the large displacement regime, pre-stresses may modify significantly the modal behaviour of structures. In this work, a geometrical nonlinear total Lagrangian formulation that includes cross-sectional deformations is developed to analyse the vibration modes of composite beams structures in the nonlinear regime. Equations of motion are solved around nonlinear static equilibrium states, which are identified using a Newton–Raphson algorithm along with a path-following method of arc-length type. Different boundary conditions and stacking sequences are analysed. It is shown that vibration modes are strongly modified by nonlinear phenomena. Moreover, models that do not describe those effects accurately may results in misleading results, especially if compression is dominant. In fact, results show a crossing phenomenon in the post-buckling regime of an asymmetric cross-ply beam, whereas it is completely unforeseen by the linearized analysis.

On a planar theory of a discrete nonlinearly elastic rod

A discrete model for elastic rods undergoing planar motions based on the theory of a directed (or Cosserat) rod is presented. Edge vectors and a director are used to capture cross section deformations including stretch, stretch gradients, shear, shear gradients, and the Poisson effect. In addition, deformations such as longitudinal stretch and bending are also incorporated. The model is validated with the help of known analytical solutions to benchmark problems using Green and Naghdi’s rod theory.

Rate effect in inclined fibre pull-out for smooth and hooked-end fibres: a numerical study

Based on a numerical model to simulate the static behaviour of a smooth fibre extracted from a cementitious matrix, a rate dependent friction law, widely used in earthquake engineering for steady-state slip phenomena, is proposed to capture the rate effect observed in dynamic pull-out tests for both smooth and hooked-end fibres. After calibrating the friction coefficients with the experimental results of smooth fibres, the model is subsequently applied to predict the pullout behaviour of both smooth and hooked-end fibres at different inclination angles ($$0^{\circ }$$, $$30^{\circ }$$ and $$60^{\circ }$$) loaded at three different velocities (0.01, 0.1 and 1 mm/s). The global tendency of all the pull-out curves was captured, fibre’s cross sectional deformations were also reproduced remarkably well. Moreover, the developed model helps to cast light on the different mechanisms related to the pull-out process.

A Novel Approach to Perform the Identification of Cross-Section Deformation Modes for Thin-Walled Structures in the Framework of a Higher Order Beam Theory

This paper presents a novel approach to identify cross-section deformation modes for thin-walled structures by assembling preliminary deformation modes (PDM) considering their participation in free vibration modes. These PDM, defined over the cross-section through kinematic concepts, are integrated in the governing equations of a higher order model and then uncoupled in the form of generalized eigenvectors. The eigenvectors are deemed to inherit the attributes of structural behaviours and can serve as the basis to assemble PDM. Accordingly, a criterion was developed to handle the eigenvectors, pursuing (i) the clustering of PDM that participate in a same structural behaviour, (ii) the assignation of the corresponding weights that indicate their participation and (iii) the decomposition of an amplitude function when it is related to several structural behaviours. Moreover, a numbering system was proposed to hierarchically organize the deformation modes, which is conducive to a reduced higher order model. The main features of this approach are found in its ability to be performed in a more operational way and its nature to give deformation modes physical interpretation inherited from the dynamic behaviours. The versatility of the approach was validated through both numerical examples and comparisons with other theories.

Dynamics of variable length geometrically exact beams in three-dimensions

We investigate the three-dimensional dynamics of a variable-length, geometrically-exact beam. The beam is released / retracted from a guide. Geometrically exact beam theory, like regular beam theory, is phrased in terms of the deformation of a neutral axis and the rotations of the cross-sections normal to the neutral axis. In contrast to beams in linear elasticity, geometrically exact beams allow large rotations of the beam’s cross-section and large deformations of the line of centroids. We derive the necessary governing equations for the system which, in three dimensions, contain non-trivial contributions from three-dimensional rotations coupled to the varying length of the cable. These equations are then solved through a Galerkin finite element method, after first mapping the physical domain to a fixed computational domain. Large rotations are incorporated into the finite element procedure by utilizing the exponential representation of the rotation tensor. Finally, as an important application of our computational formulation, we investigate the three-dimensional dynamics of a spinning, vibrating, variable-length, flexible beam through a sequence of increasingly complex examples.

A GBT-based mixed finite element for curved thin-walled members with circular axis

Abstract In this paper a mixed finite element based on Generalised Beam Theory (GBT) is proposed to analyse the first-order behaviour of naturally curved beams with circular axis (without pre-twist) and having deformable thin-walled cross-sections. The element applies the assumed strain concept to the longitudinal strains terms that are not present in straight members and cause locking. The additional strain DOFs are condensed out and therefore the stiffness matrix of the mixed element shares the DOFs of the standard (displacement-based) GBT finite element. The superior predictive capacity of the proposed mixed element with respect to the standard element with reduced integration is demonstrated through several examples involving complex global-distortional-local cross-section deformation.

Mechanical properties prediction of 3D angle-interlock woven composites by finite element modeling method

A new 3D finite element model (FEM) is established based on the actual microstructure of 3D angle-interlock woven composites, considering the configuration of outer yarns, yarns cross-sectional deformation of and spatial orientation. A prediction of the meso-scale mechanical response and effective elastic properties of 3D angle-interlock woven composites have been presented to verify the validation of 3D FEM. The effects of woven parameters on the mechanical properties are investigated in detail. The results show that 3D FEM precisely simulates the spatial geometric characteristics of 3D angle-interlock woven composites. The reasonable overall stress fields and local stress distribution can be identified and well support the strength prediction. It is convenient to predict all the elastic constants of 3D angle-interlock woven composites with different parameters simultaneously using 3D FEM. The calculated results show that 3D angle-interlock woven composites have good mechanical properties and can be considered as anisotropy materials in a macro-scale. In addition, the warp yarn density, weft yarn density and fiber volume fraction are important factors affecting the mechanical properties of 3D angle-interlock woven composites.

Homogenization assumptions for coupled multiscale analysis of structural elements: beam kinematics

This contribution proposes a multiscale scheme for structural elements considering beam kinematics. The scheme is based on a first-order homogenization approach fulfilling the Hill–Mandel condition. Within this paper, special focus is given to the transverse shear stiffness. Using basic boundary conditions, the transverse shear stiffness drastically depends on the size of the representative volume element (RVE). The reason for this size dependency is identified. As a consequence, additional internal constraints are proposed. With these new constraints, the homogenization scheme leads to cross-sectional values independent of the size of the RVE. As they are based on the beam assumptions, a homogeneous material distribution in the length direction yields optimal results. Furthermore, outcomes of the scheme are verified with simple linear elastic benchmark tests as well as nonlinear computations involving plasticity and cross-sectional deformations.

A Novel 2D Probability Density Function Integrating the Rectal Motion and Wall Thickness in Prostate IMRT

Background and purposeThis study investigated the variations of rectal motion and wall thickness in prostate intensity-modulated radiotherapy using a novel 2D probability density function. To evaluate the impact of the position, thickness, and deformation of the rectum on the dose distribution in prostate intensity-modulated radiotherapy plans, probability density functions (pdf) of the deformation of rectal cross-section (DW), rectal dose distribution (RM), and changes in rectal wall thickness (TW) were used in the planning optimization. Materials and MethodsThe problem of approximating the product of a number of Gaussian mixture distributions arises in the number of parameters describing the specific mean value, standard deviation, and weight in every Gaussian. In this work, a pdf model has been developed which specifies the variability of the average rectal wall thickness. The model is based on the histogram of 587 randomly selected patients with prostate cancer. ResultsThe average wall thicknesses were determined based on the rectal structure contours drawn on the planning CT image set of the patient. The pdf describing the variability of the rectal wall thickness (pdfTW) is represented as a three-mode Gaussian mixture of specific (μF,σF); (μPF,σPF) and (μE,σE) and individual weights (wF, wPF, and wE) representing full, partially full, and empty rectal states, respectively. ConclusionA 2D Gaussian pdf of rectal motion and rectal thickness (2D pdfM&TW) function, as a product-mixture model of the pdf of the rectal motion (pdfM) and the pdfTW, was developed using published and experimental data, respectively, and presented mathematically. Using correlation values between the functions pdfM and pdfTW, the sensitivity of profiles and projections to the 2D pdfM&TW is numerically demonstrated.

A visco-elastic GBT-based finite element for steel-concrete composite beams

Abstract This paper reports the latest developments concerning the use of Generalised Beam Theory (GBT) in the field of steel-concrete composite beams. In particular, a GBT-based finite element is presented that uses a linear visco-elastic material law to capture, accurately and efficiently (with a very low computational cost), the effects of concrete creep, as well as cross-section distortion and shear lag in complex cross-sections (combining closed cells and open branches). It is shown that the versatility of the GBT approach makes it possible to obtain accurate solutions with a fairly small number of cross-section deformation modes (cross-section DOFs), leading to significant computational savings with respect to standard shell finite element models. Several numerical examples are presented, to illustrate the capabilities and potential of the proposed GBT-based finite element.

ПРОГНОЗИРОВАНИЕ РИСКОВ ЗАКЛИНИВАНИЯ ДЛЯ ИСКЛЮЧЕНИЯ ВОЗМОЖНОСТИ ПРИХВАТОВ ТЕХНИЧЕСКОЙ СИСТЕМЫ «ПЕРФОБУР» ПРИ БУРЕНИИ РАЗВЕТВЛЕННЫХ КАНАЛОВ В ТЕРРИГЕННЫХ КОЛЛЕКТОРАХ

Актуальность. Одним из перспективных методов вторичного вскрытия продуктивных пород является бурение глубоких каналов малого диаметра технической системой радиального бурения «Перфобур». Рассмотрены вопросы прогнозирования и предупреждения прихватов бурильных компоновок технической системы вследствие возможного заклинивания в интервалах неустойчивых пород. Заклинивания в данных интервалах с большой степенью вероятности происходят вследствие упруговязкопластического деформирования поперечного сечения перфорационного канала. Цель: оценка рисков прихватов технической системы «Перфобур» вследствие заклинивания при бурении и спускоподъемных операциях и разработка технологических мероприятий по их предупреждению. Объекты: глубокий канал малого диаметра и сверхмалого радиуса кривизны в терригенном пласте-коллекторе нефтяного месторождения в Поволжье, представляющего собой чередование аргиллита, алевролита и песчаника. Методы: геомеханическое моделирование, численное интегрирование, метод переменных модулей. Результаты. Определены перемещения стенок глубокого перфорационного канала во времени для терригенного пласта-коллектора, представляющего собой чередование аргиллита, алевролита и песчаника. Получены зависимости упруговязкопластического перемещения стенок канала малого диаметра (58–60 мм) и радиуса кривизны (5–10 м) с изменением зенитного угла. Упруговязкопластическое перемещение верхней стенки перфорационного канала, как правило, значительно (в 1,5 и более раза) превышает упруговязкопластическое перемещение боковой стенки перфорационного канала. Следовательно, упруговязкопластическое перемещение верхней стенки является наиболее опасным и определяющим с точки зрения заклинивания особенно при спускоподъемных операциях. При бурении долотами типа PDC (опасное перемещение стенки равно 2 мм) определено, что наиболее опасным с точки зрения заклинивания является пропласток аргиллита и время безопасного ведения работ составляет один час. Для предупреждения возможного заклинивания компоновок технической системы «Перфобур» предложено применение специально разработанного секционного винтового забойного двигателя габарита 49 мм с кинематическим отношением рабочих органов – 9:10, что кратно увеличивает механическую скорость бурения по сравнению ранее применяемыми (также не серийными) винтовыми забойными двигателями с кинематикой рабочих органов – 5:6, использование струйных и волновых кольмататоров, расширителей, калибраторов-виброгасителей и осцилляторов, размещаемых в расчетных местах компоновки низа бурильной колонны для предотвращения и ликвидации возможных осложнений в радиальных каналах.

Experimental Study on Residual Cross-Sectional Flattening of Thin-Walled Pipes Under Pure Plastic Bending

Abstract Cross-sectional ovalization (ovalization) usually occurs when thin-walled pipe is subjected to large plastic bending. This paper is concerned with residual deformation of thin-walled pipe's cross section in a radial direction when external bending moment is removed. In order to clarify the fundamental ovalization characteristics, find out what factors influence the residual flattening (value of ovalization), the ovalization behavior is investigated experimentally. The experiments are carried out on 21 stainless steel specimens with different geometric parameters under different bending radii by means of a four-point pure bending device. The residual cross-sectional flattenings are monitored continuously by scanning the cross section periodically along the circumferential direction. From the experimental results, it is observed that the cross-sectional shape of the thin-walled pipe is not perfect standard ellipse, and the appearance of the maximum residual flattening is usually found in the direction normal to the neutral surface. It is also revealed the relationships between the residual flattening and the bending radius, the wall thickness, and the pipe outer diameter, i.e., the residual flattening increases as the bending radius and the wall thickness reduce, but it increases as the outer diameter increases. These results are expected to find their potential application in thin-walled pipe bending operation.

Design of structural steel members by advanced inelastic analysis with strain limits

Structural steel design is traditionally a two step process: first, the internal forces and moments in the structure are determined from a structural analysis. Then, a series of design checks are carried out to assess the strength and stability of individual members. The structural analysis is typically performed using beam finite elements, which are usually not able to capture local buckling explicitly. Instead, the assessment of local buckling and rotation capacity is made through the concept of cross-section classification, which places class-specific restrictions on the analysis type (i.e. plastic or elastic) and defines the cross-section resistance based on idealised stress distributions (e.g. the plastic, elastic or effective moment capacity in bending). This approach is however considered to be overly simplistic and creates artificial steps in the capacity predictions of structural members. A more consistent approach is proposed herein, whereby a second-order inelastic analysis of the structure or structural component is performed using beam finite elements, and strain limits are employed to mimic the effects of local buckling, control the spread of plasticity and ultimately define the structural resistance. The strain limits are obtained from the continuous strength method. It is shown that not only can local buckling be accurately represented in members experiencing uniform cross-sectional deformations along the length, but, by applying the strain limits to strains that are averaged over a defined characteristic length, the beneficial effects of local moment gradients can also be exploited. The proposed method is assessed against benchmark shell finite element results on isolated members subjected to bending, compression and combined loading. Compared to conventional steel design provisions and even to existing advanced design approaches utilising second-order elastic analysis, the proposed design approach provides consistently more accurate capacity predictions.