Ovalization Of Cross-section Research Articles

Osteology and relationships of the Late Triassic giant dicynodont Lisowicia

Abstract Unexpectedly abundant remains of herbivorous therapsids in the Late Triassic strata of southern Poland have significantly supplemented knowledge of their evolution. The skeletal morphology of the Late Norian (or Rhaetian) dicynodont Lisowicia bojani supports its close relationship to the Carnian Woznikella, both known from the Polish part of the Germanic Basin. Three evolutionary lineages of dicynodonts—Laurasian–Gondwanan Rhadiodromus klimovi → Jachaleria candelariensis lineage, Laurasian lineage Shaanbeikannemeyeria xilougouensis → Lisowicia bojani, and the Gondwanan lineage Kannemeyeria simocephalus → Dinodontosaurus brevirostris—are distinguished based on characters of cranial and postcranial elements. In the lineages characterized by the parietal oval in cross-section and the two distinct articulations on the sternum, there is a tendency to exclude the frontal from the orbital margin and to reduce the number of sacral vertebrae. In the lineage with the parietal narrow and triangular in cross-section, the frontal forms part of the orbit margin, there is a single joint on the sternum, and there is a tendency towards flattening the skull roof. In both lineages the shoulder girdle is convergently modified, the acromion process decreased, and joints on the sternum moved posteriorly.

Prediction of sectional collapse of thin-walled structure under pure bending by nonlinear composite beam theory

Brazier (1927) found that when one dimension of the beam cross-section was relatively smaller than the others, large in-plane displacements over the cross-section might occur, even though the strains could remain very small. Under this circumstance, the so-called Brazier effect refers to the cross-sectional ovalization, which leads to nonlinear bending buckling and collapses. This paper studies the Brazier effect by the nonlinear Variational Asymptotic Beam Sectional Analysis (VABS) theory which considers finite cross-sectional deformations. Nonlinear VABS reduces three-dimensional (3D) continuum to a one-dimensional (1D) beam analysis and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities without unnecessary kinematic assumptions. The present theory is implemented using the finite element method (FEM) in the VABS code, a general-purpose beam cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model using the Euler–Bernoulli beam theory. The deformation gradient tensor is directly used to deal with finite deformation, various strain definitions, and several types of material laws. Numerical examples demonstrate the capabilities of VABS to predict the sectional collapse of thin-walled structures under pure bending.

Morphological Ontogeny, Ecology, and Biogeography of Fuscozetes fuscipes (Acari, Oribatida, Ceratozetidae).

The systematic status of Fuscozetes Sellnick, 1928, is not clear in the literature. Therefore, the morphological ontogeny of F. fuscipes (C.L. Koch, 1844), the type species of this genus, was investigated and compared with its congeners in this study, and a new diagnosis of Fuscozetes is given. The juveniles of F. fuscipes are light brown, with a brown prodorsum, sclerites, epimeres, and legs. In all juveniles, a humeral organ and a humeral macrosclerite are present. The gastronotum of the larva has 12 pairs of setae (h3 is present), whereas the nymphs have 15 pairs. In the larva, the gastronotal shield is weakly developed, and most gastronotal setae are short except for a slightly longer h2. Most of the gastronotal setae are inserted on the microsclerites except for h3, and several other macrosclerites and many microsclerites are present on the hysterosoma. In the nymphs, the gastronotal shield is well developed, with 10 pairs of setae (d-, l-, and h-series, and p1), and setae p2 and p3 are located on a large posteroventral macrosclerite. In all the instars, femora I and II are oval in cross-section, without a large ventral carina. Mitochondrial COI sequence data revealed a deep split between the Nearctic and Palearctic populations of F. fuscipes, and a less, but significant, divergence within each continent. These strong geographical barriers were contrasted with multiple cases of shared haplotypes over long distances in the Palearctic, indicating high migration rates in modern times.

Study on cross-section distortion behaviors for tube bending at varying geometry parameters

Tube bending is often plagued by the critical forming defect of cross-section distortion, which increases flow resistance, affects the strength and stiffness of bent-tube, and thus directly influences the usage performance of bent-tube components. To achieve accurate tube bending forming, the distortion behaviors for cross-section during tube bending should be clarified. A finite element (FE) model accounting for the change in elastic modulus was employed for addressing the distortion behaviors of the cross-section for high strength 0Cr21Ni6Mn9N (0Cr21Ni6Mn9N-HS) tube in NC rotary draw bending at varying geometry parameters. The findings indicate that accounting for the change in elastic modulus can aggrandize the distortion ratio of the cross-section, but has no significant impact on the distortion behaviors for the cross-section. The cross-section ovality behaviors of the 0Cr21Ni6Mn9N-HS tube at various geometry parameters for NC rotary draw bending have been clarified, and the ranges of sound parameters have been determined.

A novel numerical framework to simulate mechanical response and damage characteristics of mountain tunnels under faulting

This paper presents a novel numerical framework that can simulate the mechanical response and damage characteristics of mountain tunnels under faulting more precisely and efficiently. Both the submodeling and two-stage models are adopted in the framework. The submodeling technique is used to obtain a precise simulation of tunnel-fault interaction while ensuring computational efficiency. The two-stage models can acquire accurate initial stress of the tunnel lining and simulate the tunnel-rock interaction during fault movement, which can also achieve the transition from static to dynamic analysis. The computational efficiency can be improved by about 73 % via the proposed numerical framework compared to the conventional numerical analysis when keeping the same mesh sizes. Moreover, overall lining damage indices and cross-sectional ovalization are introduced to quantitatively evaluate the respective damage and deformation of the tunnel lining cross-section, and damage level classifications for tunnel lining under faulting are established. Parametric sensitivity analyses are performed to investigate key factors affecting the mechanical damage behavior of mountain tunnels under strike-slip faulting, including fault dislocation, fault zone width, and the tunnel-fault intersection angle. The increasing fault dislocation causes larger tunnel-rock interaction around the fault plane, making the damage and deformation of tunnel lining around the fault plane more severe. The fault zone width has a significant impact on the damage and deformation range of tunnel lining. The tunnel-fault intersection angle contributes great influence on the magnitude and range of tunnel lining damage and deformation. The tunnel lining would suffer relatively severe damage and deformation when the two fault blocks move away from each other along the tunnel axial.

Performance assessment of buried steel pipelines reinforced with carbon fibre-reinforced polymer under reverse fault movement

Buried oil and gas pipelines are often affected by the active zones across faults, and the failure of pipeline functions owing to relative fault movements has attracted widespread attention. Carbon fibre-reinforced polymer (CFRP) was proposed as a reinforcement measure for buried continuous pipelines crossing faults to mitigate the structural damage to pipelines subjected to large permanent ground deformations. In this study, the lamina model and Hashin failure criterion were used to simulate the CFRP material in a three-dimensional nonlinear finite element model of the pipeline-soil interaction. The peak strain and cross-sectional ovalization of the pipeline were used to quantify the nonlinear response of the steel pipeline subjected to reverse fault movement. Parametric studies in terms of the CFRP wrapping angle, thickness, length, as well as internal pressure were conducted to comprehensively assess overall performance of CFRP-wrapped steel pipelines. Results indicated that the CFRP wrapping in direction of 0°/90° with respect to the axial direction of the pipeline exhibit the optimum effects in improving the performance of pipelines. For steel pipelines subjected to reverse fault, increase of the CFRP wrapping thickness effectively reduces the development of compressive strain on the pipeline wall, thereby delay the local buckling failure of the pipeline. Besides, CFRP is effective in increasing the bending curvature radius and preventing the local buckling of the pipeline, but insufficient wrapping length of CFRP can lead to local buckling of steel pipelines under same fault displacement. For pipelines with internal pressures internal pressure can enhance the overall performance of CFRP wrapped pipelines against reverse fault movement.

The use of MCDM techniques to assess fluid pressure on the bending quality of AA6063 heat-treated tubes

This paper investigates the bending of aluminum tubes under different fluid pressure and heat treatment conditions. The application of multi-criteria decision-making (MCDM) methods was evaluated for selecting the best forming condition considering cross-section ovality, thinning, and thickening of the bent tubes. Analytic hierarchy process (AHP) was used for criteria weighting, and technique for order of preference by similarity to ideal solution (TOPSIS) and multi-objective optimization on the basis of ratio analysis (MOORA) were used for alternative ranking. A combination of various types of AA6063 tubes, including as-received (R), annealed (O), and artificial aged (T6), with different fluid pressures (0, 1, 1.8, 3.2, and 3.6 MPa) were assumed to be as the alternatives (forming conditions). The results demonstrate that the ovality and thickening of the bent tubes decrease by increasing the internal fluid pressure. On the other hand, increasing the internal fluid pressure gives rise to an increase in thinning of bent tubes. The O sample has the lowest ovality and thickening while the T6 sample has the lowest thinning. MCDM analysis revealed that the O samples at higher pressures show better bendability.

Centrifuge tests of large-diameter steel pipes crossing strike–slip faults

Fault rupture is one of the main hazards for buried continuous pipes, and it has frequently been investigated experimentally in recent decades. In this study, to explore and model the failure mechanisms of continuous steel pipes crossing faults, a series of centrifuge tests of large-diameter steel pipes (D = 1.616 m) crossing strike–slip faults was conducted. Pipe strains are measured using 30 strain gauges, and pipe cross-section deformation is determined using a micro industrial endoscope for the first time; thus, cross-sectional ovalization is accurately derived. Subsequently, factors influencing the responses of steel pipe crossing faults, such as the burial depth, pipe-fault crossing angle, and pipe diameter, are investigated. The centrifuge test results show that the pipe responses, including the pipe strain and deformation, are significantly affected by these factors. Finally, three limit states are considered and compared: 3 % tensile strain, 15 % cross-sectional ovalization, and local buckling limit, and pipe failure behaviors are examined for these cases. The results shown that these tests can serve as benchmarks for theoretical and numerical models.

Analysis of failure modes in pipe-in-pipe repair systems for water and gas pipelines

Different failure modes should be carefully analyzed to effectively design the pipe-in-pipe (PIP) repair systems to rehabilitate natural gas and water pipelines in place and in service. This study characterizes the failure modes through analytical and numerical modelling of the different performance objectives to have a comprehensive understanding of the overall behavior of PIP systems with a range of thicknesses and elastic moduli. It focused on assessing the structural performance of PIP systems under different load actions including vibration/fatigue due to traffic loads, lateral deformation, cross-section ovalization, axial stresses and thermal deformation, internal pressure, and impact. The results of the analyses showed that the thickness and elastic modulus significantly affect the failure modes of PIP systems. The implemented Analytical Hierarchy Process (AHP) suggested that lateral deformation is the most critical failure mode followed by internal pressure based on global priority as well as both criteria (thickness and elastic modulus) when the design pressure is 200 psi with the cross-section ovalization the least critical failure mode of the PIP systems. The results of this study provide useful predictive modelling techniques and preliminary design tools for PIP systems for new material systems development and/or evaluation of the suitability of the available PIP systems for pipeline repair.

Geometrically nonlinear formulation of Generalized Beam Theory for the analysis of thin-walled circular pipes

In this paper, the formulation of Generalized Beam Theory (GBT) for the geometrically nonlinear analysis of thin-walled circular pipes is presented. GBT is a computationally efficient numerical method which is especially formulated for thin-walled members with a capacity of determining the cross-sectional deformation through a combination of a set of pre-determined cross-sectional deformation modes. In this study, the current GBT analysis of circular pipes which is limited to buckling analysis is enhanced to a full geometrically nonlinear analysis. This new formulation considers the nonlinear membrane kinematic description based on the Green–Lagrange strain definition. The nonlinear tangent stiffness matrices and the internal force vectors are derived from the variation of the internal energy which results in third and fourth-order GBT deformation mode coupling tensors. These tensors can predetermine the type of GBT deformation modes needed for the nonlinear analysis based on the applied loading conditions. In addition to the classical GBT deformation modes, the non-conventional GBT deformations modes have a vital role since without these modes the coupling tensors and the nonlinear stiffness matrix related to the transverse and the shear membrane energy will be lost. Here, to illustrate the application and capabilities of the developed GBT formulation, two numerical examples involving transverse and longitudinal bending are presented to show the nonlinear relationship between bending, cross-sectional ovalization, and higher local deformation modes. For the purpose of validation, these examples are compared with refined shell finite element models in both displacement and stress fields.

Баклаги салтівської культури в збірці Дніпропетровського національного історичного музею імені Дмитра Яворницького

Проаналізовано колекцію баклаг кінця VIII – першої половини ІХ століття, виготовлених нагончарному крузі, зі збірки Дніпропетровського національного історичного музею імені ДмитраЯворницького. Ці вироби салтівської культури – специфічний і малочисельний тип посуду. Доколекції увійшли три баклаги ІХ століття, знайдені на території колишньої Катеринославськоїгубернії та м. Дніпра, а також одна баклага, передана 2010 року з с. Лобойківка Петриківськогорайону Дніпропетровської області. Проаналізовано відмінності між зразками цього загаломтипового посуду. Подано відомості про аналогії цим посудинам, знайдені на пам’ятках степовогота лісостепового варіантів салтівської культури. Among the antiquities of the Saltiv culture there is a specific and non-numerical type of ceramicutensils – water bottles or flasks, which were used to transport a small amount of liquid.The article deals with three water bottles of the late 8th – early 9th centuries, which are stored in thefunds of the Dmytro Yavornytsky National Historical Museum of Dnipro and one water bottle, which wastransferred to the museum from the village of Loboykivka of the Petrykivka District of the DnipropetrovskRegion in 2010. The location of one of these water bottles is unknown. One of them has been found in thegrated former Ekaterinoslav Government, and the second one has been found in 1958 at the mouth ofthe Shiyanka river, now it’s a territory of the city of Dnipro. All four vessels have a curved front surface,a flat or slightly concave back surface, a cylindrical body, a high throat (lost in one water bottle), formedseparately and then attached to the main part of the vessel, two handles, oval in cross section, fixed onopposite sides from the throat. One water bottle is decorated with a pentagonal star in a round medallion,and two – with medallions. The medallions are formed from the same clay as the water bottle itself. Onthe water bottle, found in 2010, there are remnants of a color ornament. These are elements applied withbrown, light brown paint and white engobes.The article also analyzes the differences between different samples of this mostly the same type ofutensils – the shape of the crown, the shape of the handles, the ornament (or lack thereof). The authorconcludes that these differences are not enough to distinguish certain types and kinds of this crock.The described water bottles are characteristic of the antiquities of the Saltiv culture and havea number of analogies on the monuments of its steppe and forest-steppe variants – settlements, nomadicstations, cemeteries, as well as in the form of accidental finds. They were made in the workshops of theCrimea to order of the steppe and forest-steppe population, most likely for horsemen. Mostly made of thesame clay as amphorae and in the same workshops. But there are single water bottles that are made ofanother clay mass with the addition of chalk and hardness. It is possible that they are not made in Crimeanworkshops, but are imitations of these forms by local craftsmen.Water bottles from the Dmytro Yavornytsky National Historical Museum of Dnipro complementa number of already known and published vessels and expand the range of their existence.

A FEA Method for Mathematical Calculation and Prediction Analysis Cross-sectional Ovalization of Tubes under Rotary Straightening

The section flattening phenomenon (namely Bazier effect) will occur in the large bending deformation stage of thin-walled pipe in the continuous straightening process. The maximum section flattening amount and the residual section flattening amount are important process parameters, which are the basis for calculating the subsequent process parameters of the flattening circle, and directly determine the roundness of the final pipe and the product quality. However, it is hard to be obtained by the theoretical or experimental methods. Therefore, based on the structure and process parameters of the leveler, a finite element model was built to simulate the section flattening process. Then, ANSYS/LS-DYNA software was used to dynamically simulate the bending flattening phenomenon of thin-walled pipe in the continuous straightening process, and the stress and strain nephographic of the flattening deformation zone was obtained. By recording the position curve of the key nodes in the preventing process, the section flattening amount of the thin-walled pipe in the large bending deformation stage in the continuous straightening process was determined. The simulation results show that the dynamic simulation method can effectively predict the section flattening of thin-walled pipe in the process of continuous straightening.

Process parameter optimization for thin-walled tube push-bending using response surface methodology

In this paper, the response surface methodology (RSM) and finite element (FE) simulation were applied to optimize the push-bending process parameters of the thin-walled tube with polyurethane mandrel. The objective of the present work is to predict the optimal set of process parameters including the length to diameter ratio of the mandrel (L/D), the friction coefficient between die and tube ( $${\mu }_{1}$$ ), the friction coefficient between polyurethane and tube ( $${\mu }_{2}$$ ), and Poisson’s ratio of polyurethane ( $$\upsilon$$ ) to obtain qualified bent tubes. Three empirical models were developed to describe the relationship between process parameters and quality parameters of the bent tubes. In addition, the significant factors affecting the forming quality were analyzed using analysis of variance (ANOVA) of each model. Response surfaces were constructed to study the effect of each process parameter on the quality of the bent tubes. Finally, the process optimization window with the maximum thinning rate ( $$\varphi$$ ) less than 20%, the maximum thickening rate ( $$\psi$$ ) less than 17%, and the maximum cross-section ovality ( $$\xi$$ ) less than 5% of the bent tube was established. Qualified bent tubes with diameter of 144 mm, wall thickness of 2 mm, and bending radius of 280 mm were formed experimentally by following the established process window.

Influence of tectonic stress on the structural safety of mountain tunnel under the strike-slip faulting

The distribution of tectonic stress around the fault is very complicated, which may affect tunnel behavior under the dislocation of fault. Therefore, this paper aims to investigate the influence of tectonic stress on the structural safety of mountain tunnel under the strike-slip faulting. Variable lateral stress coefficients from 0.3 to 3.0 are considered via a series of three-dimensional finite element models. Safety assessment indices based on the overall lining damage in compression/tension and the ovalization of the tunnel cross-section are used to evaluate the damage of tunnel structure subjected to fault movement quantitatively. The results show that the cross-sectional damage and ovalization of tunnel lining mainly distribute around the fault plane, and the tectonic stress plays a crucial role in the tunnel’s response to strike-slip faulting. With the increasing lateral pressure coefficient, both the value and distribution scope of the cross-sectional compressive damage in the longitudinal direction increase; while the value and distribution of cross-sectional tensile damage decrease when the coefficient is larger than 1.0, and its damage is slighter than compressive damage. The cross-sectional ovalization of the tunnel is also significantly affected by the lateral pressure coefficient, especially when the coefficient is larger than 1.0.

Closed-form solution for free vibration of variable-thickness cylindrical shells rotating with a constant angular velocity

Based on the classical Donnell’s and Love’s shell theories, free vibration behavior of variable-thickness thin cylindrical shells rotating with a constant angular velocity is analyzed. The equations of motion and corresponding boundary conditions of rotating homogenous cylindrical shells with axisymmetric variation of thickness are derived using Hamilton’s principle. This formulation includes effects of initial hoop tension due to the centrifugal force as well as Coriolis and centrifugal accelerations. Considering the variation of stiffness coefficients in axial direction, the classical Love’s theory results in a coupled system of two second-order and one fourth-order partial differential equations with variable coefficients in terms of kinematic variables. The Galerkin’s method is used to obtain a closed-form expression of sixth-order frequency equation with coefficients in terms of rotation speed (Ω) for with boundary conditions. The natural frequencies of stationary and rotating cylindrical shells with constant thickness, as special cases, are validated with existing ones in the literature. Case studies are presented for three different patterns of thickness variation in forms of arbitrary power, axisymmetric modal and stepwise functions. It is seen that the influence of thickness variation on the natural frequencies and mode shapes is a function of different parameters including rotation speed, boundary conditions, and geometric ratios, especially this effect is much more pronounced for cantilever long shells with a high rotation speed. Also, differences in results predicted by the Donnell’s and Love’s theories become larger for long and cantilever shells in vibration mode shape corresponding to (m=1,n=2), i.e., the ovalization of cross section.

Numerical Simulations and Experimental Study on the Reeling Process of Submarine Pipeline by R-Lay Method

During the reeling process of the reel-lay method, the pipe will be subjected to combined loading of tension and bending. Excessive ovalization of the pipe will affect the structural performance and even lead to structural instability of the pipe. In this paper, a numerical simulation model of the pipe-reeling process is established by finite element tools. The Ramberg–Osgood material model is used to study the ovalization and bending moment of the pipe cross-section during the pipe-reeling process based on the Von Mises plasticity and nonlinear kinematic hardening rules. The results show that the ovalization and bending moment of the pipe section will change significantly during the pipe-reeling process. Subsequently, one set of 6-inch pipe-reeling experimental setups was designed to conduct a full-scale experiment. Compared with the experimental results, the feasibility of the finite element model is verified. Finally, the effects of diameter-to-thickness ratio, the material parameters of the pipe, and the pipe axial tension on the ovalization and bending moment changes are studied. Research shows that each parameter has a certain influence on the pipe of the reeling process, and the diameter-to-thickness ratio of the pipe has the most obvious effect. When the diameter-to-thickness ratio decreases, the bearing capacity for bending moments and the ability to resist ovalization of pipe are enhanced. At the same time, each parameter has a significant impact on the reeling process of the pipeline.

A redescription of Lophorhothon atopus (Ornithopoda: Dinosauria) from the Late Cretaceous of Alabama based on new material1

Diagnostic dinosaur fossils of the southeastern United States are rare discoveries, and even more precious are those fossils that preserve a large portion of a skeleton. Sixty years ago, the dinosaur Lophorhothon atopus was described from Upper Cretaceous sediments of Alabama. It then represented the oldest, most complete, dinosaur in the southeastern United States. Based on a reexamination of the holotype material and a new specimen collected from the same beds, we provide a new diagnosis of this taxon. In particular, the solid nasal crest has several autapomorphies including caudally projecting frontal processes that are oval in cross section, meaning that they did not coalesce at the midline. Other autapomorphies are found on the prefrontal and squamosal. Combining the two Lophorhothon specimens provides nearly the entire skeleton for phylogenetic analysis, which we find as a hadrosauromorph just outside of Hadrosauridae. The original diagnosis of this taxon included the frontonasal fontanelle as a distinguishing character, but comparing the many examples of frontonasal openings across hadrosauromorph taxa shows that in at least a few species, such as Lophorhothon, the structures should be considered a frontonasal fenestra instead of a fontanelle. Additionally, the notion that dinosaurs from the East Coast of the United States represent primitive relicts is an idea that originated before many of the European and Asian hadrosauromorphs known today had been discovered. With new dating and phylogenetic information, it appears that Appalachian dinosaurs are on par evolutionarily with most of the global community and the term ”relict fauna” should be abandoned.

Simple equations for strength and deformability verification of tubular steel wind turbine towers

Simple analytical expressions for a preliminary design of tubular steel wind turbine towers under flexure and shear are proposed. Expressions derived included local buckling effects, shear to moment interaction, ovalization of cross-section and inelastic rotation of foundation. A finite-element analysis with ABAQUS program was also conducted for examination of the ovalization effects and for the whole response of steel tube in flexure.Numerical and analytical results were compared with the experimental results of recent studies available in the literature, showing good agreement. The range of variable investigated refers to medium and large size steel wind tower with cylindrical shape having: - length to diameter ratio between 10 and 50; - diameter to thickness ratio between 100 and 300; - height to diameter of plinth ratios between 4 and 6.Ultimate (ULS) and service limit (SLS) states were considered to derive the geometrical characteristic of steel tube (diameter and thickness at the base) taking into account of main aspect concerning the structural behavior of wind towers. The paper also highlights the necessity to improve both experimental and analytical research to develop specific recommendation and expressions for hand calculation of these kinds of structures necessary for a quick preliminary design of these structures.Original contribution of research was the derivation of simple analytical expressions for strength and deformability verification taking into account of cross-section ovalization, shear to moment interaction, and P-Δ effects, all phenomenon generally considered with 3D non linear finite element analyses.

Numerical Study of the Use of Tyre-Derived-Aggregate (TDA) as the Backfill Above Flexible PVC Pipeline

Tyre Derived Aggregates (TDA), produced by shredding scrap car tyres, show many interesting features, such as: durability, low bulk density, thermal insulation, good drainage properties or ability to damp vibrations, which makes them a useful material for civil engineering. One of the possible applications is the partial filling of excavations with TDA during the construction of underground pipelines in order to decrease the load applied on the pipe. The article presents results of a multivariate numerical study of 2D FEM models of a flexible PVC pipe - soil system, in which the presence of a mixture of sand and TDA (tyre chips - 40% by weight) (STCh) in the backfill was simulated. The models differed in the thickness of the STCh layer (t = 0 – 0.9 m) and inclination of the excavation walls (a trench with vertical walls or open excavations with 3:1 and 1:1 slopes). The main goal of the numerical analyses, performed by means of the Z_Soil.PC program, were to investigate the effect of the presence of the softer STCh layer in the backfill zone on the pipe deformation (relative deflection δ/D) and internal forces in the pipe wall. The soil was simulated with the use of either the Hardening Soil Small (HSS) or Coulomb-Mohr (CM) constitutive model with the parameters’ values estimated based on results of laboratory tests (published by researchers from Wollongong University). The PVC pipe was modelled as linear elastic. The results of the analyses show that, due to enhanced arching, STCh layer of the optimum thickness t = 0.55 m can effectively reduce δ/D when used in the backfill of the trench. It can also decrease the difference between the maximum and minimum bending moment in the pipe wall, leading to less ovalization of the pipe cross-section. This positive effect diminishes if the width of excavation is larger, as the model is gradually transforming towards the positive projecting conduit type. The CM model gives underestimated values of the pipe deformation and internal forces. Though, in the case of lack of all the HSS parameters’ values, it is better to use the CM model with E = E 50 than E = E ur as it gives a better approximation of pipe behaviour.

Generalized Beam Theory formulation for thin-walled pipes with circular axis

In this paper, the linear Generalized Beam Theory (GBT) is formulated for stress and deformation analysis of curved thin-walled circular pipes. In comparison to the analysis of straight pipes, the analysis of pipe bends is a complex problem due to the strong coupling effect of the longitudinal bending, warping and the cross-sectional ovalization. GBT is a beam theory especially formulated for thin-walled sections with the capacity of determining the cross-sectional deformation through the combination of a set of predetermined cross-sectional deformation modes. This nature of GBT makes it suitable to precisely identify and determine possible couplings between the considered GBT deformation modes and to analyze the behavior of pipe bends with high accuracy and computational efficiency. The formulation presented in this paper is based on Kirchhoff’s thin-plate assumption with consideration of additional shear deformation modes to overcome null transverse extension and shear membrane strain assumptions of classical GBT formulations. Here, to illustrate the application and capabilities of the developed GBT formulation, a set of numerical examples with in-plane, out-of-plane and pressure loading conditions involving a combination and coupling of bending, warping, torsional, axisymmetric and local deformations are presented. For the purpose of validation, these examples are compared with refined shell finite element models in both displacement and stress fields.