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.

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.

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.

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＇.

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.

Variable-stiffness composite cylinder design under combined loadings by using the improved Kriging model

The large design freedom of variable-stiffness (VS) composite material presupposes its potential for wide engineering application. Previous research indicates that the design of VS cylindrical structures helps to increase the buckling load as compared to quasi-isotropic (QI) cylindrical structures. This paper focuses on the anti-buckling performance of VS cylindrical structures under combined loads and the efficient optimization design method. Two kinds of conditions, bending moment and internal pressure, and bending moment and torque are considered. Influences of the geometrical defects, ovality, on the cylinder's performances are also investigated. To increase the computational efficiency, an adaptive Kriging meta-model is proposed to approximate the structural response of the cylinders. In this improved Kriging model, a mixed updating rule is used in constructing the meta-model. A genetic algorithm (GA) is implemented in the optimization design. The optimal results show that the buckling load of VS cylinders in all cases is greatly increased as compared with a QI cylinder.

Study on Deformation Law of Circular Foundation Under Combined Loading

The foundations of some ocean engineering structures are built to withstand not only the vertical gravity load V, but also the horizontal load H induced by sea waves and current. The horizontal load includes the concentrated force load, the moment load M, and the torque load T termed also as combined loading. It is of academic and engineering significance to study the deformation law of submarine seabed due to combined loading. On the basis of the three-dimensional elastic mechanics solution of circular foundation, numerical methods are used to analyze the deformation law of submarine soil under circular foundation with six degrees of freedom. The finite element analysis results give the elastic deformation law of soil in three dimensional spaces, modify the theoretical elasticity solution, and presents nonlinear soil deformation mechanism under the circular foundation with six degrees of freedom.

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.

A HALF PLANE CRACK UNDER THREE-DIMENSIONAL COMBINED MODE IMPACT LOADING

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 suddenly-applied shear line loads is consid- ered. The analytic expression for the combined mode stress intensity factors as a function of time is obtained. The method of solution is based on the application of integral transforms and the Wiener-Hopf technique. Some features of the solutions are discussed and graphical numerical results are presented.

General Analytical Shakedown Analysis of a Structure Subjected to Combined Loading with Constant and Cyclic Loads

The shakedown behavior of structures subjected to a combined loading of constant and cyclic loads has been well researched.For some specified problems,shakedown limit loads have been obtained.However,the general effect of combined loading on the structural shakedown has not yet been presented.The general analytic solution of the elastic shakedown limit load is thus derived for a structure subjected to combined loading.Polizzotto's extended static shakedown theorem for combined loading is applied.The stress field in equilibrium with the external constant load required in Polizzotto's extended theorem is constructed by subtracting the reference elastic stress field of the peak cyclic load from the elastic-plastic stress field of the combined constant load and peak cyclic load.The shakedown condition of the stress field is then derived according to the extended theorem.Through the analytical analysis of the shakedown condition,the structural shakedown behavior under combined loading is investigated.A general solution of the shakedown limit load is then derived,and the effects of the combined loading on the shakedown behavior are proposed.The obtained general analytical result is applied to a hollow tension specimen under constant tension and alternating torsion and a plate with a central hole under constant and cyclic tension.The results are consistent with the solutions reported in the literature.

A New Fracture Criterion for a Crack under Combined Mode Loading

A new fracture criterion was proposed. The physical explanation of the criterion is that crack will propagate when the minimum strain energy density in iso hoop stress curve reach a critical strength of the material considered. The resulting curve of critical fracture of mixed mode cracks shows that the present fracture is efficient and more accurate than the previous criteria.

局部冲刷下砂土中桩-盘复合基础V-H组合承载特性

海上风电基础除承受复杂组合荷载作用外,也受波流冲刷作用.为探讨局部冲刷对砂土地基中V-H联合加载下单桩-摩擦盘复合基础承载特性的影响,基于自行设计的室内水槽试验装置,完成了一系列冲刷及模型载荷试验,获得了复合基础冲刷前后的荷载-位移曲线,经无量纲化处理与曲线拟合,得到复合基础承载包络线及其简化计算公式.计算结果表明:局部冲刷作用使复合基础的竖向及横向抗力明显降低,削弱程度分别约12.1%和26.9%.进一步分析表明:存在一个最优预加竖向荷载(V),其对复合基础的极限横向承载力起到最显著的增强效果;此外,局部冲刷作用导致V-H联合受荷单桩-摩擦盘复合基础的承载包络线明显向内收缩,所提出的简化计算公式可供工程应用参考.

上砂下黏地层中桩-筒复合基础V-H承载特性

海上风机基础不仅受自重等竖向力V作用,也因水流、波浪和风等影响而承受水平荷载H。为探讨上砂下黏地层中一种由单桩和吸力筒组成的新型海上风机桩-筒复合基础受V-H组合作用时的承载特性,自主设计完成了一系列室内桩-筒复合基础V-H组合加载模型试验,获得不同组合参数下桩-筒复合基础的荷载-位移曲线和桩身弯矩分布曲线,并绘制出V-H承载力包络线。在此基础上,采用ABAQUS建立了上砂下黏地层中桩-筒复合基础三维数值分析模型,经模型验证与参数分析,进一步讨论了砂土厚度、筒径、筒高以及加载高度等参数对桩-筒复合基础承载特性的影响曲线,并拟合出桩-筒复合基础承载力简化计算公式,分析结果表明:桩-筒复合基础能显著提高桩身水平承载力,增幅达30%~90%,且增加筒径比增加筒高更有利于提高基础水平承载力;上部砂土层较厚时,桩-筒复合基础存在一个使复合基础水平承载力达到最大的预加竖向荷载最佳值,其值随不同载荷工况在(0.4~0.7)Vult范围内变化。

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.

Effects of water intrusion and loading rate on mechanical properties of and crack propagation in coal–rock combinations

Tackling the problems of underground water storage in collieries in arid regions requires knowledge of the effect of water intrusion and loading rate on the mechanical properties of and crack development in coal–rock combinations. Fifty-four coal–rock combinations were prepared and split equally into groups containing different moisture contents(dry, natural moisture and saturated) to conduct acoustic emission testing under uniaxial compression with loading rates ranging from 0.1 mm/min to 0.6 mm/min. The results show that the peak stress and strength-softening modulus, elastic modulus, strain-softening modulus, and post-peak modulus partly decrease with increasing moisture content and loading rate. In contrast, peak strain increases with increasing moisture content and fluctuates with rising loading rate. More significantly, the relationship between stiffness and stress, combined with accumulated counts of acoustic emission, can be used to precisely predict all phases of crack propagation. This is helpful in studying the impact of moisture content and loading rate on crack propagation and accurately calculating mechanical properties. We also determined that the stress thresholds of crack closure, crack initiation, and crack damage do not vary with changes of moisture content and loading rate, constituting 15.22%, 32.20%, and 80.98% of peak stress, respectively. These outcomes assist in developing approaches to water storage in coal mines, determining the necessary width of waterproof coal–rock pillars, and methods of supporting water-enriched roadways, while also advances understanding the mechanical properties of coal–rock combinations and laws of crack propagation.

Mechanical performance of rock bolts under combined load conditions

Rock bolts are subjected to different loading conditions along their lengths such as axial,bending,and/or shear forces,which can cause failure at lower loads than those considered for design purposes.The common existing methodologies do not consider the actual loading of the rock bolts and assume it is only pure axial or pure shear.This study was conducted to investigate the un-grouted rock bolt performance under combined load conditions.Two loading regimes were evaluated:the effect of initial shear displacement on axial load capacity and displacement,and the effect of axial displacement on the shear load capacity.The first regime was also conducted for shear with a gap,when there is a spacing between the shear interfaces.The results of this study showed that the rock bolt can resist higher axial loads than shear under pure or combined load conditions.Under combined load conditions,the rock bolt capacity decreased significantly for both regimes.However,when applying the shear load with a gap,the rock bolt load capacity was not affected significantly.Also,the total bar deformation was improved for shear and axial.The findings of this study show the need to improve the rock bolt design considering the complex loading conditions in situ with/without a gap.

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.

Elastoplastic solutions for single piles under combined vertical and lateral loads

为了改进单身者的设计和计算的可靠性，堆在下面联合了垂直、侧面的负担，答案基于路基反应方法，最终的土壤抵抗在被考虑被介绍，路基反应的系数被假定是一个常数。相应计算节目用 FORTRAN 语言被开发。在获得的答案和模型测试结果之间的比较被做显示出获得的答案的有效性。，计算结果显示有垂直、侧面的负担和上面的堆积长度的增加的最大的侧面的排水量和弯曲时刻增加磨擦了作为堆积僵硬，路基反应的系数和土壤增加的让步的排水量减少。堆积头条件控制堆积回答，这也被显示出，垂直负担可以引起不稳定性问题到堆积。一般来说，建议方法能被采用计算堆积偏转的大小的堆积回答独立人士。

Method for Calculating the Ultimate Strength of Pitting Corrosion Ship Structural Plates Under Combined Loads

In order to solve the problem of calculating the ultimate strength of marine plate under pitting corrosion,the plate taking from marine with pitting corrosion was studied. Based on the data of pitting corrosion recorded,the concept of pitting corrosion characteristic element matrix was proposed to describe the distribution and the forms of pitting. Moreover,the model of sensitivity calculation was established to analyse the sensitivity of pitting corrosion characteristic elements for the ultimate bearing capacity of ship structural plate. A new approach was proposed to calculate the ultimate strength of pitting damaged ship structural plate under combined loads based on the factor of rigidity reduction. Simultaneously this new approach was proven to be validated by finite element simulation. Finally,formula of ultimate strength of pitting damaged ship hull plate was established by series of numerical calculations based on the approach,and the reliability of the formula was validated as well.