Reliability analysis of marine risers with narrow and long corrosion defects under combined loads

A marine riser,one of the most important components of offshore oil/gas transportation,needs to be designed to eliminate the risks caused by complex ocean environments,platform displacement and internal corrosion,etc.In this study,a new analytical-numerical assessment approach is proposed in order to quantitatively investigate the reliability of internally corroded risers under combined loads including axial tension and internal pressure.First,an analytical solution of the limit state function of intact risers under combined loads is obtained,which is further modified by the non-dimensional corrosion depth （d/ t） for the risers with a narrow and long corrosion defect.The relationship between d/t and limited internal pressure is obtained by finite element analysis and nonlinear regression.Through an advanced first-order reliability method （HL-RF） algorithm,reliability analysis is performed to obtain the failure probability,the reliability index and the sensitivity.These results are further verified by Monte-Carlo importance sampling.The proposed approach of reliability analysis provides an accurate and effective way to estimate the reliability of marine risers with narrow and long corrosion defects under combined loads.

Analytic elasticity solution of bi-modulus beams under combined loads

A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. The example analysis shows that the maximum tensile stress using the same elastic modulus theory is underestimated if the tensile elastic modulus is larger than the compressive elastic modulus. Otherwise, the maximum compressive stress is underestimated. The maximum tensile stress using the material mechanics solution is underestimated when the tensile elastic modulus is larger than the compressive elastic modulus to a certain extent. The error of stress using the material mechanics theory decreases as the span-to-height ratio of beams increases, which is apparent when L/h ≤ 5. The error also varies with the distributed load patterns.

Dynamic response of UHMWPE plates under combined shock and fragment loading

Ultra-high molecular weight polyethylene(UHMWPE)fiber composite has been extensively used to construct lightweight protective structures against ballistic impacts,yet little is known about its performance when subjected to combined blast and fragment impacts.Built upon a recently developed laboratory-scale experimental technique to generate simulated combined loading through the impact of a fragment-foam composite projectile launched from a light gas gun,the dynamic responses of fullyclamped UHMWPE plates subjected to combined loading were characterized experimentally,with corresponding deformation and failure modes compared with those measured with simulated blast loading alone.Subsequently,to explore the underlying physical mechanisms,three-dimensional(3D)numerical simulations with the method of finite elements(FE)were systematically carried out.Numerical predictions compared favorably well with experimental measurements,thus validating the feasibility of the established FE model.Relative to the case of blast loading alone,combined blast and fragment loading led to larger maximum deflections of clamped UHMWPE plates.The position of the FSP in the foam sabot affected significantly the performance of a UHMWPE target,either enhancing or decreasing its ballistic resistance.When the blast loading and fragment impact arrived simultaneously at the target,its ballistic resistance was superior to that achieved when subjected to fragment impact alone,and benefited from the accelerated movement of the target due to simultaneous blast loading.

LARGE DEFLECTION PROBLEM OF CIRCULAR PLATES WITH VARIABLE THICKNESS UNDER THE ACTION OF COMBINED LOADS

By using the modified iteration method of large deflection theory of plates with variable thichness[1], we solve the problem of circular plates with variable thickness subjected to combined loads under the boundary conditions of the clamped edges and get comparatively more accurate second-order approximate analytical solution. If the results of this paper are degraded into the special cases, the results coinciding with those of papers [1,2] can be obtained. In this paper, the characteristic curves are plotted and some comparisons are made. The results of this paper are satisfactory.

Combined load bearing capacity of rigid piles embedded in a crossanisotropic clay deposit using 3D finite element lower bound

In this study,an iterative-based three-dimensional finite element lower bound in association with the second-order cone programming method is adopted to evaluate the limit load of a single pile embedded in cross-anisotropic soils under general loading condition.The lower bound solutions of the pile embedded in an anisotropic soil deposit can be found by formulating the element equilibrium,equilibrium of shear and normal stresses along discontinuities,boundary conditions,yield function,and optimizing the objective function through the second-order cone programming method in conjunction with an iterative-based update procedure.A general loading condition is considered to profile the expansion of the safe load in the vertical-horizontal-moment(V-H-M)space.The results of this study are compared and validated against three different cases including an isotropic lateral loading,anisotropic end bearing capacity,and a pile embedded in an isotropic soil deposit under general loading condition.A parametric study is conducted to evaluate the impact of different influencing factors.It was found that the effect of anisotropy on the variation of lateral limit load of a single pile is more pronounced than the corresponding vertical and bending moment limit loads,whereas the interface properties have more significant effects on the vertical and bending moment limit loads in comparison to the lateral limit load.

Transformation Matrix for Combined Loads Applied to Thin-Walled Structures

This paper transforms combined loads, applied at an arbitrary point of a thin-walled open section beam, to the shear centre of the cross-section of the beam. Therein, a generalized transformation matrix for loads with respect to the shear centre is derived, this accounting for the bimoments that develop due to the way the combined loads are applied. This and the authors’ earlier paper (World Journal of Mechanics 2021, 11, 205-236) provide a full solution to the theory of thin-walled, open-section structures bearing combined loading. The earlier work identified arbitrary loading with the section’s area properties that are necessary to axial and shear stress calculations within the structure’s thin walls. In the previous paper attention is paid to the relevant axes of loading and to the transformations of loading required between axes for stress calculations arising from tension/compression, bending, torsion and shear. The derivation of the general transformation matrix applies to all types of loadings including, axial tensile and compression forces, transverse shear, longitudinal bending. One application, representing all these load cases, is given of a simple channel cantilever with an eccentrically located end load.

Fatigue Life of Slewing Bearings under Combined Radial,Axial and Tilting Moment Loads

A calculation method of fatigue life for slewing bearings under combined radial, axial and tilting moment loads was proposed. Single row four-point contact ball slewing bearing being used as a case, the statics model of the slewing bearing was established and a set of equilibrium equations were obtained. By solving the equilibrium equatioas, the rolling element loads were obtained and the equivalent rolling element loads were calculated further. By using the geometrical parameters of the bearing, the rating rolling element loads were calculated, and the fa- tigue life of the bearing was calculated by using the rating rolling element loads and the equivalent rolling element loads. A calculation example shows the feasibility of the proposed method.

Mechanical responses of anchoring structure under triaxial cyclic loading

Dynamic load on anchoring structures(AS)within deep roadways can result in cumulative damage and failure.This study develops an experimental device designed to test AS under triaxial loads.The device enables the investigation of the mechanical response,failure mode,instability assessment criteria,and anchorage effect of AS subjected to combined cyclic dynamic-static triaxial stress paths.The results show that the peak bearing strength is positively correlated with the anchoring matrix strength,anchorage length,and edgewise compressive strength.The bearing capacity decreases significantly when the anchorage direction is severely inclined.The free face failure modes are typically transverse cracking,concave fracturing,V-shaped slipping and detachment,and spallation detachment.Besides,when the anchoring matrix strength and the anchorage length decrease while the edgewise compressive strength,loading rate,and anchorage inclination angle increase,the failure intensity rises.Instability is determined by a negative tangent modulus of the displacement-strength curve or the continued deformation increase against the general downward trend.Under cyclic loads,the driving force that breaks the rock mass along the normal vector and the rigidity of the AS are the two factors that determine roadway stability.Finally,a control measure for surrounding rock stability is proposed to reduce the internal driving force via a pressure relief method and improve the rigidity of the AS by full-length anchorage and grouting modification.

Study on Failure Mechanism and Bearing Capacity of Three-Dimensional Rectangular Footing Subjected to Combined Loading

This paper presents two kinematic failure mechanisms of threc-dimensional rectangular footing resting on homogeneous undrained clay foundation under uniaxial vertical loading and uniaxial moment loading. The failure mechanism under vertical loading comprises a plane strain Prandti-type mechanism over the central part of the longer side, and the size of the mechanism gradually reduces at the ends of the longer side and over the shorter side as the corner of rectangular footing is being approached where the direction of soil motion remains normal to each corresponding side respectively. The failure mechanism under moment loading comprises a plane strain scoop sliding mechanism over the central part of the longer side, and the radius of scoop sliding mechanism increases linearly at the ends of the longer side. On the basis of the kinematic failure mechanisms mentioned above, the vertical ultimate bearing capacity and the ultimate bearing capacity against moment or moment ultimate bearing capacity are obtained by use of upper bound limit analysis theory. At the same time, numerical analysis results, Skempton＇ s results and Salgado et al. ＇s results are compared with this upper bound solution. It shows that the presented failure mechanisms and plastic limit analysis predictions are validated. In order to investigate the behaviors of undrained clay foundation beneath the rectangular footing subjected to the combined loadings, numerical analysis is adopted by virtue of the general-purpose FEM software ABAQUS, where the clay is assumed to obey the Mohr-Coulomb yielding criterion. The failure envelope and the ultimate bearing capacity are achieved by the numerical analysis results with the varying aspect ratios from length L to breadth B of the rectangular footing. The failure mechanisms of rectangular footing which are subjected to the combined vertical loading V and horizontal loading H （Vertical loading V and moment loading M, and horizontal loading H and moment loading M respectively are observed in the finite element analysis. ） is explained by use of the upper bound plasticity limit analysis theory. Finally, the reason of eccentricity of failure envelope in H-M loading space is given in this study, which can not be explained by use of the traditional ＇ swipe test＇.

Buckling analysis of shear deformable composite conical shells reinforced by CNTs subjected to combined loading on the two-parameter elastic foundation

The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic foundation(T-P-EF).It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs,based on a generalized first-order shear deformation shell theory(FSDST)which includes shell-foundation interaction.By adopting the extended mixing rule,the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters.Three carbon nanotube distribution in the matrix,i.e.uniform distribution(U)and V and X-types linear distribution are taken into account.The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads(CBLs)of the structure selected here.The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF.Finally,a parametric study is carried out to study the influences of the foundation parameters,the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs.

Undrained Bearing Capacity of Spudcan Under Combined Loading

The bearing capacities of spudcan foundation under pure vertical （/1）, horizontal （H）, moment （M） loading and the combined loading are studied based on a series of three-dimensional finite element analysis. The effects of embedment ratio and soil non-homogeneity on the bearing capacity are investigated in detail. The capacities of spudcan under different pure loading are expressed in non-dimensional bearing capacity factors, which are compared with published results. Ultimate limit states under combined loading are presented by failure envelopes, which are expressed in terms of dimensionless and normalized form in three-dimensional load space. The comparison between the presented failure envelopes and available published numerical results reveals that the size and shape of failure envelopes are dependent on the embedment ratio and the non-homogeneity of the soil.

Failure Loci of Suction Caisson Foundations Under CombinedLoading Conditions

Suction caissons are widely used to support offshore fixed platforms in coastal areas. The loadings transferred to suction caissons include the eccentric lateral force induced by waves and self weight of the platform structure. However, under this kind of combined loading conditions, the failure mechanism of caissons with shallow embedment depths is quite different from conventional deep foundations or onshore shallow footings. The behaviour of caissons subjected to combined loadings may be described with the ＂failure locus＂ in force resultant spaces. Here the failure loci of smooth caissons are studied by use of finite dement approach, with the embedment ratio of caissons varying in the range of 0.25 - 1.0 and eccentricity ratio of horizontal loadiugs in 0 - 10. The platform settlement and tilt limits are involved into determination of failure loci, thus the platforms can avoid significant displacements for the combined loadings located inside the failure locus. Three families of loading paths are used to map out the locus. It is found that the shape of failure loci depends on 3 non-dimensional parameters, and the failure locus of a given caisson changes gradually from the elliptical curve to hooked curve with increasing shear strength of soil. The lateral capacity of short caissons may be enhanced by vertical forces, compared with the maximum lateral capacity of long caissons occurring at the vertical force being zero. The critical embedment ratios partitioning elliptical and hooked loci are proposed.

Postbuckling of Imperfect Stiffened Cylindrical Shells Under Combined External Liquid Pressure and Axial Compression

posthuckling analysis is presented for the stilTened cylindrical shell of finite length subjected to combined loading of external liquid pressure and axial compression. The formulations are based on a boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, nonlinear large deflections in the postbuckling range and initial geometrical imperfections of the shell. The 'smeared stifl'cner' approach is adopted for the stiffencrs. In the analysis a singular perturbation technique is used (o determine the interactive buckling loads and the postbuckling paths. Numerical examples cover the performance of perfect and imperfect, stringer and ring stiffened cylindrical shells. Typical results arc presented in the dimcnsionless graphical form.

Space decomposition based parallelization solutions for the combined finiteediscrete element method in 2D

The combined finiteediscrete element method （FDEM） belongs to a family of methods of computationalmechanics of discontinua. The method is suitable for problems of discontinua, where particles aredeformable and can fracture or fragment. The applications of FDEM have spread over a number of disciplinesincluding rock mechanics, where problems like mining, mineral processing or rock blasting canbe solved by employing FDEM. In this work, a novel approach for the parallelization of two-dimensional（2D） FDEM aiming at clusters and desktop computers is developed. Dynamic domain decompositionbased parallelization solvers covering all aspects of FDEM have been developed. These have beenimplemented into the open source Y2D software package and have been tested on a PC cluster. Theoverall performance and scalability of the parallel code have been studied using numerical examples. Theresults obtained confirm the suitability of the parallel implementation for solving large scale problems. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

POSTBUCKLING OF IMPERFECT STIFFENED CYLINDRICAL SHELLS UNDER COMBINED EXTERNAL PRESSURE AND HEATING

A postbuckling analysis is presented for a stiffened cylindrical shell of finite length subjected to combined loading of external pressure and a uniform temperature rise. The formulations are based on a boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, nonlinear large deflections in the postbuckling range and initial geometrical imperfections of the shell. The 'smeared stiffener' approach is adopted for the stiffeners. The analysis uses a singular perturbation technique to determine the interactive buckling loads and the postbuckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, stringer and ring stiffened cylindrical shells. Typical results are presented in dimensionless graphical form.

THE THREE-DIMENSIONAL STRESS INTENSITY FACTOR UNDER MOVING LOADS ON THE CRACK FACES

The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body,with the crack faces subjected to a traction distribution consisting of two pairs of combined mode point loads that move in a direction perpendicular to the crack edge is considered.The analytic expression for the combined mode stress intensity factors as a function of time for any point along the crack edge is obtained.The method of solution is based on the application of integral transform together with the Wiener-Hopf technique and the Cagniard-de Hoop method. Some features of the solution are discussed and graphical results for various point load speeds are presented.

Analysis and design for the comprehensive ballistic and blast resistance of polyurea-coated steel plate

Fragments and blast waves generated by explosions pose a serious threat to protective structures.In this paper,the impact resistance of polyurea-coated steel plate under complex dynamic loading is analyzed and designed for improving comprehensive ballistic and blast resistance using the newly established computational evaluating model.Firstly,according to the thickness and placement effects of the coating on the impact resistance,the steel-core sandwich plates are designed,which are proved to own outstanding comprehensive ballistic and blast resistance.Besides,the distribution diagram of ballistic and blast resistance for different polyurea-coated steel plates is given to guide the design of protective structures applying in different explosion scenarios.Furthermore,the dynamic response of designed plates under two scenarios with combined fragments and blast loading is studied.The results show that the synergistic effect of the combined loading reduces both the ballistic and blast resistance of the polyurea-coated steel plate.Besides,the acting sequence of the fragments and blast affects the structural protective performance heavily.It is found that the first loading inducing structural large deformation or damage is dominant.When fragments impact first,the excellent unit-thickness ballistic performance of the structural front part is strongly needed for improving the comprehensive ballistic and blast resistance.

Influence of Vertical Load on Lateral-Loaded Monopiles by Numerical Simulation

Monopiles are the most common foundation form of offshore wind turbines,which bear the vertical load,lateral load and bending moment.It remains uncertain whether the applied vertical load increases the lateral deflection of the pile.This paper investigated the influence of vertical load on the behaviour of monopiles installed in the sand under combined load using three-dimensional numerical methods.The commercial software PLAXIS was used for simulations in this paper.Monopiles were modelled as a structure incorporating linear elastic material behaviour and soil was modelled using the Hardening-Soil(HS)constitutive model.The monopiles under vertical load,lateral load and combined vertical and lateral loads were respectively studied taking into account the sequence of load application and pile slenderness ratio(L/D;L and D are the length and diameter of the pile).Results suggest that the sequence of load application plays a major role in how vertical load affects the deflection behaviour of the pile.Specifically,when L/D ratios obtained by lengthening the pile while keeping its diameter constant are 3,5 and 8,the relationships between lateral load and the deflection behaviour of the pile under the effect of vertical load demonstrate a similar trend.Furthermore,the cause of increased lateral capacity of the pile under the action of applied vertical load in the common practical application case and in the VPL case was analyzed by studying the variation law of soil stress along the pile embedment.Results confirm that the confining effect of vertical load increases means effective stress of the soil around the pile,thus increasing soil stiffness and pile capacity.

Investigation on the Folding Mode and Deployment Process of an Inflatable Boarding Platform for the Marine Emergency Evacuation System

Monopiles are the most common foundation form of offshore wind turbines,which bear the vertical load,lateral load and bending moment.It remains uncertain whether the applied vertical load increases the lateral deflection of the pile.This paper investigated the influence of vertical load on the behaviour of monopiles installed in the sand under combined load using three-dimensional numerical methods.The commercial software PLAXIS was used for simulations in this paper.Monopiles were modelled as a structure incorporating linear elastic material behaviour and soil was modelled using the Hardening-Soil(HS)constitutive model.The monopiles under vertical load,lateral load and combined vertical and lateral loads were respectively studied taking into account the sequence of load application and pile slenderness ratio(L/D;L and D are the length and diameter of the pile).Results suggest that the sequence of load application plays a major role in how vertical load affects the deflection behaviour of the pile.Specifically,when L/D ratios obtained by lengthening the pile while keeping its diameter constant are 3,5 and 8,the relationships between lateral load and the deflection behaviour of the pile under the effect of vertical load demonstrate a similar trend.Furthermore,the cause of increased lateral capacity of the pile under the action of applied vertical load in the common practical application case and in the VPL case was analyzed by studying the variation law of soil stress along the pile embedment.Results confirm that the confining effect of vertical load increases means effective stress of the soil around the pile,thus increasing soil stiffness and pile capacity.

Assessment of the stiffened panel performance in the OTEC seawater tank design:Parametric study and sensitivity analysis

Ocean thermal energy conversion(OTEC)is a process of generating electricity by exploiting the temperature difference between warm surface seawater and cold deep seawater.Due to the high static and dynamic pressures that are caused by seawater circulation,the stiffened panel that constitutes a seawater tank may undergo a reduction in ultimate strength.The current paper investigates the design of stiffening systems for OTEC seawater tanks by examining the effects of stiffening parameters such as stiffener sizes and span-over-bay ratio for the applied combined loadings of lateral and transverse pressure by fluid motion and axial compression due to global bending moment.The ultimate strength calculation was conducted by using the non-linear finite element method via the commercial software known as ABAQUS.The stress and deformation distribution due to pressure loads was computed in the first step and then brought to the second step,in which the axial compression was applied.The effects of pressure on the ultimate strength of the stiffener were investigated for representative stiffened panels,and the significance of the stiffener parameters was assessed by using the sensitivity analysis method.As a result,the ultimate strength was reduced by approximately 1.5%for the span-over-bay ratio of 3 and by 7%for the span-over-bay ratio of 6.