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In this paper, an extended exponential-polynomial-closure (EPC) procedure is presented to investigate the transient probability density function (PDF) of stochastic oscillator under the stimulation being modulated white noise based on the conventional EPC approach. By the presented EPC procedure, an evolutionary exponential–polynomial function is defined as the PDF solution and a set of evolutionary independent base functions are introduced to span a [Formula: see text] space. By integrating the residual error with those evolutionary functions spanning the [Formula: see text] space, a group of ordinary differential equations can then be formulated. Three nonlinear oscillators are analyzed numerically and the results comparisons of various techniques validate the presented EPC procedure in solution efficiency and accuracy, particularly in the PDF solution tails which play a crucial role in reliability analysis. The transient PDF solutions acquired by the presented EPC procedure match well with Monte Carlo simulation even in the PDF solution tails, whereas the solutions obtained by the equivalent linearization are deemed to be unacceptable for the strongly nonlinear oscillators subjected to modulated stimulation. Notably, the presented EPC procedure can highly increase the computational efficiency by about 1[Formula: see text]000 times in all the presented numerical examples in comparison to Monte Carlo simulation.

Textile reinforced mortar (TRM) composites are an innovative solution for strengthening existing structures. TRM composites are produced with high-strength textile embedded in inorganic mortar matrices, demonstrating compatibility with existing masonry. As TRM is externally bonded to the surface of the structure, the bond behaviour between TRM and masonry substrate is a critical issue to investigate. In this study, experimental research aims to deeply understand the bond behaviour of TRMs for strengthening masonry structures. The experiments mainly consist of a series of single-lap shear bond tests on TRMs to masonry substrates. Two types of textiles (carbon and steel textile) combined with two mortar matrices (cement and lime-based mortar) were used to construct TRM. The effect of the textile and mortar matrix is presented. The test results are discussed in terms of the full range of load-slip responses and failure modes. The result showed that TRM with steel textile and cement-based mortar matrix offers better bond behaviour, but the risk of masonry damage should also be considered.

The rounded corners have significant influences on the buckling processes and carrying capacity of thin-walled steel structures. This paper was intended to investigate the influences of rounded corners on the performance of single-coped beam with slender web. The mechanical behaviours of two typical single-coped beams with different coped depths were experimentally investigated first. The finite element (FE) model was proposed and the accuracy was verified by comparing it with the experimental results. Based on the proposed FE model, the influences of different radius for rounded corners ( R c ) were investigated. It was concluded that the application of rounded corners has great impacts on the failure modes and buckling processes of single-coped beams. It was also found that the energy-dissipating capacity as well as load carrying capacity increased significantly with the application of round corners, especially for single-coped beam with deep coped depth. The round corner index, which considered the influences of both rounded corner and coped depth, was proposed via fitting with the simulational results. A typical design example considering the round corner index was also provided and a more accurate result was achieved.

Composite materials that are constructed of textiles with high mechanical strength and embedded in a mortar matrix (also known as textile reinforced mortars (TRMs)) have received significant attention as they are a promising material for strengthening historical masonry structures because of their superior sustainability and physical compatibility with masonry substrates. In this paper, three types of TRMs, which include steel, carbon and basalt textiles embedded in cement mortar matrices used as shear reinforcement of masonry panels, are experimentally investigated. The experimental component consists of the mechanical characterization of TRMs by testing 16 TRM coupons under tensile loading, and evaluation of their strengthening effect on the shear behaviour of an unreinforced masonry wall by testing 2 unreinforced and 5 strengthened masonry panels under diagonal compression loading. Finally, the contribution of TRM in strengthened panel is evaluated by analytical methodologies and a criterion to design the TRM for strengthening masonry wall is proposed.

Historic buildings have significant cultural, scientific, and aesthetic value, and show the accomplishments of past eras. Unfortunately, many of wooden historic buildings are destroyed by f...

Textile reinforced mortar (TRM) composites have received much attention as they are a superior sustainable material and physically compatible with masonry and historical structures. Among the numerous materials used in TRM composites, steel reinforced grout (SRG) which is produced with high strength steel cords embedded in a cementitious mortar matrix, demonstrates exceptional mechanical performance at a relatively low cost. In this paper, an experimental investigation is carried out on their use as in-plane shear reinforcement of masonry wall panels. The masonry panels are constructed with grey clay bricks (GCBs), a unique construction material widely used in traditional Chinese architecture. Diagonal compression tests are carried out on two unreinforced panels and six strengthened panels with different reinforcement configurations. The contribution of the SRG system to strengthening is assessed by examining the shear stiffness, shear strength, ductility under shear, and changes in failure mechanisms. A comparative analysis is carried out by using results from the previous literature, and the analytical methodologies and the practical use of the SRG system are also discussed.

The steel coped beams are commonly seen in steel structures since slotting and coping are inevitable for the fitting of steel beams. The steel coped beams with slender web, however, are prone to local web buckling, which results in decreased load carrying capacity and catastrophic failure modes. This paper is intended to investigate the feasibility of reinforcing single-coped beam with carbon fiber reinforced polymer (CFRP) plate. Totally five single-coped steel beams with or without CFRP plate reinforcement were tested. The failure processes and influences of different parameters were discussed and compared. It was found that the application of CFRP plate is effective to prohibit the development of buckling line. Thus, the load carrying capacity of CFRP reinforced single-coped beam could be three times higher than its control group. A novel finite element (FE) model was proposed and verified with experimental results. Based on the FE model, the failure mechanisms of CFRP reinforced single-coped beam were investigated. The parameter analysis was also conducted to acquire the optimal size of the CFRP plate considering its reinforcement effects. Based on both experimental and simulational results, the simplified design method of CFRP reinforced single-coped beam was also proposed.

Forced vibration of two-dimensional functionally graded beams is studied in this paper by a developed meshfree boundary-domain integral equation method. Material properties of the functionally graded beams are assumed varying continuously either in longitudinal or transvers direction following the exponential function. The boundary-domain integral equations are derived by using the elastostatic fundamental solutions based on the two-dimensional elastic theory. Radial integral method (RIM) is employed to transform the domain integrals into boundary integrals. A meshfree scheme is achieved through assuming the displacements and accelerations in the domain integrals by a combination of the radial basis function and polynomials with time dependent coefficients. Wilson-θ, Houbolt as well as two kinds of damped Newmark's algorithms are applied to accomplish the time integration. The forced vibration of the functionally graded beam subjected by the harmonic loading and transient loading are investigated in detail. Numerical examples demonstrate that the four mentioned time integral schemes are all adapted well to the developed meshfree boundary-domain integral equation method for analyzing the forced vibration of homogeneous structures. For the analysis of FG structures, it is shown that the damped Newmark's algorithm can achieve more stable and accurate results.

The application of external reinforcement with fiber reinforced polymer (FRP) to increase structural behavior of masonry structures has been a research focus area during the past decade. The near-surface mounting (NSM) technique is a relatively new retrofitting technique involves bonding FRP bars/strips insert into grooves cut into the surface of masonry. A numerical study was carried out to investigate the in-plane shear behavior of brick masonry wall strengthened with NSM FRP strips. A 2-D finite element (FE) model was used to simulate the structure behavior of strengthened masonry walls. The masonry was modeled by micro-modeling approach and FRP strips was modeled as attaching to the masonry mesh using the shear bond-slip relationships determined from experimental pull tests. The key shear behaviors of strengthened masonry wall panels in diagonal tension/shear tests was produced, including load-displacement response, crack development, and reinforcement contribution. Then, a parametric study was carried out to examine the contribution of different material and geometry property of FRP strips in the load carry capacity and shear ductility of strengthened masonry wall panels. Finally, the FE modeling for a real facade predicts the improvement of shear resistance which contributed by NSM FRP strengthening.

Due to the decline in the material strength and increase in natural loading, the need to strengthen historical masonry buildings is vital, and different techniques have been used to enhance the structural performance of those buildings. Textile reinforced mortar (TRM) composite systems are one of the newly developed techniques that has attracted increasing interest from researchers. To investigate the feasibility of the use of more eco-friendly materials in mortars, recycled glass sand (RGS) is substituted for natural river sand in the preparation of mortar used in the TRM system, as well as lime as a partial cement replacement. RGS was substituted for river sand at 50% and 100%, and lime was substituted for cement at 50%. A total of ten mix proportions were prepared. The mechanical properties of the mortar were analysed in terms of the flexural strength and compressive strength at 7 and 28 days. The results showed that the strengths tend to decrease as the lime and RGS proportion increases. There are the maximum average reductions of 40.3% in flexural strength and 60.4% in compressive strength for the samples with 50% lime replacement, and 38.3% in flexural strength and 33.8% in compressive strength for the samples with 100% RGS replacement. The discrepancies in the strength increase rate from 7 to 28 days were observed in some samples which may due to the different surface area and grading of RGS particles change the rate of hydration and porous in mortar. Then, the tensile behaviour of steel-TRM prepared with recycled glass sand with four different mix proportions were experimentally studied. The tensile behaviours of the tested coupons agreed well with the three-phase tensile behaviour. The TRM composite coupons prepared with 100% RGS and 50% lime replacement showed the maximum reductions (73.4%) of average tensile strength compare to the TRM coupons with 50% RGS replacement, which follow the trend of the mechanical behaviour of mortar. Finally, analytical and numerical models considering varying parameters related to the material properties were developed to understand the stress–strain responses and crack patterns of different TRM coupons in tension. Both analytical and macromodelling approaches are able to capture the key global tensile behaviour of TRM as a reasonable fitting was observed with regard to predicting the change in the stiffness in the three stages. The results obtained by micromodelling approach show that TRM coupons with 100% RGS show a larger reduction in the mortar tensile strength and bond fracture energy of the mortar-textile interface. The reason for these reductions might be that higher RGS replacement can be more porous in mortar and the angular edges and rough texture of the RGS, respectively.

This paper presents an approach with a modified M-integral for determining the stress intensity factors of cracked functionally graded titanium alloy (FGTA) components. A derivative term of the strain energy density with respect to the spatial coordinate is embedded in the modified M-integral to account for the effect of the varying elastic moduli of functionally graded material. The validity of the modified M-Integral is validated by comparison with the experimental results of the crack propagation of FGTA specimens that are manufactured by using three-dimensional (3D) printing. Resistance tests of the cracked FGTA specimens are simulated to investigate the effects of the controlled changes in the material properties on the residual strength and crack-tip stress intensity factor. Further simulations of the fatigue crack propagation of the cracked FGTA specimens are performed to examine the influence of the changes in the material properties on the fatigue crack propagation life and crack propagation rate. The analysis results indicate that the numerical method in this study can accurately simulate the crack propagation of FGTA specimens. At present, due to the complexity and limitations of additive manufacturing of materials with gradient variations, it is not available to manufacture fully graded components through 3D printing for experiments. Therefore, this study assumes an FGTA beam model that is a fully graded material model to examine the effect of material gradient on crack propagation.

Grey clay bricks (GCBs) are a traditional and unique masonry material for Chinese buildings, and their application is especially prevalent in traditional Chinese architectures. Despite that structural analyses of historical constructions have been a popular area of focus in recent studies, information on the behaviour of GCB masonry structures is still lacking. In this paper, a comprehensive characterization of the mechanical behaviour of GCB masonry by using experimental and numerical methods is presented and discussed. Characterization tests were primarily carried out to determine the mechanical strengths of GCB, cement-based and lime-based mortar, and the bond behaviour between them. Then, a series of tests was performed on GCB masonry prisms and panels to evaluate the compressive, flexure and shear behaviours of GCB masonry, respectively. Finally, numerical models based on the experimental results were setup and further implemented for analysing the nonlinear response of a historical unreinforced masonry building in Macau to obtain the safety level. The combined experimental and numerical investigation evaluates important parameters for the mechanical behaviour of GCB masonry and delivers updated understandings of the structural behaviour of existing GCB masonry buildings in China.

Textile reinforced mortar (TRM) composites are an innovative solution for strengthening masonry structural elements due to their effectiveness and sustainability, as well as their compatibility with masonry substrates. As TRM composites are externally bonded to the surface of structural elements, the bond behaviour at the textile-mortar matrix and mortar matrix-substrate interfaces is a critical issue that needs to be investigated. In this study, an extensive study is carried out which includes a series of experimental tests combined with advanced numerical modelling with the aim to provide a better understanding of the bond behaviour of steel-TRM composites for strengthening a specific type of masonry which made by grey clay bricks. The experiments mainly consist of 28 single-lap shear bond tests on steel-TRM strengthened masonry elements. The effect of the masonry substrate condition, configuration of the textile, mechanical properties of the mortar matrix, and length of the bond are presented. The test results are discussed in terms of the full range of load-slip responses and failure modes. Then, an advanced numerical model based on simple interfacial local bond-slip constitutive laws is validated by agreement with the experimental findings. Finally, the numerical results are also used to evaluate the effective bond length and further understand the bond behaviour.

FRCM composites based on long continuous fibres embedded in inorganic mortar matrix has been increasingly used to strengthen existing structures. The mechanical behaviour of FRCMs and their effectiveness in strengthening applications are highly dependent on the mechanical properties of the fibres and the mortar matrices. Research has revealed that the temperature and humidity of the curing environment has a pivotal impact on the development of the mechanical properties of cementitious mortar. Therefore, in this paper, the influence of the curing environment under moist or dry conditions with different temperatures on the degree of hydration and tensile strength of cementitious mortar are investigated. Then, direct tensile tests are applied to 30 steel-FRCM coupons which are cured in different environments to obtain the corresponding full range of tensile stress-strain responses. The effects of the strain measurement system, coupon size, clamping system and curing environment are investigated. Finally, the experimental tensile stress-strain response curves of the FRCM coupons are validated with the analytical results derived from the three different approaches to draw conclusions.

Textile Reinforced Mortars (TRMs) have found extensive attention for externally bonded reinforcement of masonry and historical structures. However, only few information is available regarding their mechanical properties and effectiveness in improving the seismic performance of strengthened structures. This paper presents an extensive numerical investigation on the effect of TRM composites on the nonlinear response and failure modes of masonry walls. The effect of boundary conditions and the TRM type on the performance of strengthened walls are critically discussed and presented. It is shown that the performance and failure mode of the walls can significantly change after strengthening, an important issue that should be considered at the design stage. Finally, the effect of TRM application on the nonlinear response of a large historical masonry facade in Macau is investigated and presented., The first author is grateful to the SAHC Master Programme for the grant awarded. The second author acknowledges the financial support of the Ministerio da Ciencia, Tecnologia e Ensino Superior, FCT, Portugal, under the grant SFRH/BPD/92614/2013 as well as the financial support of the European Union's Marie Curie Individual Fellowship program under REA grant agreement No. 701531., info:eu-repo/semantics/publishedVersion

In this paper, the fatigue life of cracked tubular structures subjected to remote cyclic tensile stress is studied by using the fracture mechanics and Paris’ law. To evaluate the flooded member detection, a reassessed leak-before-break approach is implemented, in which a more realistic crack development, by taking the partly through thickness crack stage into consideration, has been investigated, and that has never been reported in literature for tubular member with internal crack. Parametric study demonstrates that the time available to detect the presence of the crack in its flooded life depends particularly on the rate of accumulation of fatigue damage and on the initial length of surface crack presented. The results of the analysis have been applied by a case study of a particular offshore structure and loading situation, obtained to support inspection intervals of three years for flooded member detection. By comparing the current results with the conventional leak-before-break procedure in flooded member detection, it is found that for the situation studied in this paper, the flooded life predicted from conventional leak-before-break method for the crack is always on the safe side. Therefore, it is too conservative for setting up the inspection interval for flooded member detection.

This paper addresses the random vibrations of the oscillators with correlated external and parametric excitations being Gaussian white noises. The exponential polynomial closure method is used in the analysis, with which the probability density of the system responses is obtained. Two oscillators are analyzed. One is about the linear oscillator subjected to correlated external and parametric excitations. Another is about the oscillator with cubic nonlinearity and subjected to correlated external and parametric excitations. Numerical studies show that exponential polynomial closure method provides computationally efficient and relatively accurate estimates of the stationary probabilistic solutions, particularly in the tail regions of the probability density functions. Numerical results further show that correlated external and parametric excitations can cause unsymmetrical probabilistic solutions and nonzero means which are different from those when the external and parametric excitations are independent.

The analysis of the in-plane free vibration of the circular and annular FG disks by a meshfree boundary-domain integral equation method is presented in this paper. The material properties of the disks are assumed to vary in the radial direction obeying an exponential law. Based on the two-dimensional linear elastic theory, the motion equations of the FG disks are derived by using the static fundamental solutions. Radial integration method as an efficient tool is adopted to treat the domain integrals which are raised due to the material inhomogeneous and inertial effects. The natural frequencies and associate mode shapes are calculated for the FG disks with combinations of free and clamped boundary conditions. Parametric studies are also conducted to study the effects of the material gradients, radius ratios and boundary conditions on the frequency of the FG disks.