Dynamic equilibrium equations of composite anisotropic beams considering the effects of transverse shear deformations and structural damping

In this paper, Hamilton's principle is used to derive the dynamic equilibrium equations of composite nonprismatic beams made of anisotropic materials. The effects of transverse shear deformations and structural damping are considered. The displacements are defined on an arbitrarily selected coordinate system. For Hamilton's principle, the dynamic behavior of nonprismatic beams is characterized by two energy functions: a kinetic energy and a potential energy. The formulation uses the procedure of variational operations. The obtained dynamic equilibrium equations and natural boundary conditions are highly coupled.     

Bunch length measurement of picosecond electron beams from a photoinjector using coherent transition radiation

The bunch length of an electron beam derived from the UCLA Saturnus photoinjector has been measured using a 45° CTR foil. The sudden change of electrons boundary conditions cause them to radiate (transition radiation) with the spectral power entirely dependent upon the degree of coherency, which strongly relates to the beam size. A polarizing Michelson interferometer allowed measurement of the auto-correlation of the coherent transition radiation signal. An analysis method was developed to compensate for undetected low-frequency radiation and systematically extract the bunch length information for a specific beam model. This analysis allowed observation of pulse lengthening due to the space charge, as well as compression with the variation of the RF injection phase. The hypothesis of a satellite beam has been also tested using this analysis.     

智能CFRP加固RC梁荷载效应的实时模拟与测评

制备了4 根炭纤维复合材料(CFRP) 加固钢筋混凝土(RC) 实验梁, 并在梁内钢筋、混凝土及加固CFRP中预置了布拉格光栅光纤传感器(FBG) 和电阻应变片两种传感器。根据钢筋混凝土理论和ANSYS 有限元软件编制了实验梁受弯荷载效应模拟计算程序。实验表明, 实验梁在受弯承载过程中, 布拉格光栅光纤传感器与传统应变片有完全一致的线性关系; 模拟计算出的实验梁受拉钢筋、压区混凝土应变值及挠度与荷载的关系与CFRP 中FBG的实测值吻合较好。由于对既成RC 结构不能在内部装置传感器(会破坏结构降低抗力) , 采用智能CFRP 加固RC 结构可实现加固和实时健康测评双重功能。      

Analysis of composite beams with partial interaction using the direct stiffness approach accounting for time effects

This paper presents a modelling technique based on the direct stiffness method (DSM) to describe the behaviour in time of composite beams with partial shear interaction accounting for creep and shrinkage of the slab. The time‐dependent behaviour of the concrete is modelled using algebraic representations, such as the age‐adjusted effective modulus method and the mean stress method, while the steel joist, the reinforcement and the shear connection are assumed to behave in a linear‐elastic manner. Only one discretization (i.e. in the time domain) is required by the proposed stiffness formulations to perform a time analysis, while two discretizations (i.e. one in the time domain and the other in the spatial domain along the beam axis) are required by other modelling techniques available in the literature. The ability of the derived elements to overcome curvature locking problems observed to occur in some conventional displacement formulations is also highlighted. The proposed DSM approach is then validated against analytical solutions derived by the authors for simple structural systems. The applicability of this method for the time analysis of continuous composite beams is also illustrated. Copyright © 2008 John Wiley & Sons, Ltd.     

Analytical solution for the singular stress distribution due to V-notch in an orthotropic plate material

On the basis of general solutions of two-dimensional linear elasticity, displacement and singular stress fields near the singular point in orthotropic materials are derived in closed form expressions. According to the presented expressions, analysis formulas of displacement and singular stress fields near the tip of a V-notch under the symmetric and the anti-symmetric modes are obtained subsequently. The open literatures devoted to developing stress singularity near the tip of the V-notch in anisotropic or orthotropic materials. In this study, however, not only direct eigenequations were derived, but also the explicit solutions of displacement and singular stress fields were obtained. At the end, the correctness of the formulas of the singular stress field near the tip of the V-notch has been verified by FEM analysis.     

An efficient BEM to calculate weight functions and its application to bridging analysis in an orthotropic medium

An efficient boundary element method to calculate crack weight functions is developed. The weight function method is applied to bridging effect analysis in a single-edge notched composite specimen by using a bridging law which includes both interfacial debonding and sliding properties between fiber and matrix in ceramic matrix composites. A numerical method to solve the distributed spring model treating bridging fibers as stress distribution to close the crack surface is provided to determine the bridging stress, debond length, crack opening displacement and stress intensity factor.     

Studies of defects in the near-surface region and at interfaces using low energy positron beams

Positron annihilation spectroscopy (PAS) is a powerful probe to study open-volume defects in solids. Its success is due to the propensity of positrons to seek out low-density regions of a solid, such as vacancies and voids, and the emissions of gamma rays from their annihilations that carry information about the local electronic environment. The development of low-energy positron beams allows probing of defects to depths of few microns, and can successfully characterize defects in the near-surface and interface regions of several technologically important systems. This review focuses on recent studies conducted on semiconductor-based systems.     

Static and low-velocity impact behavior of sandwich beams with closed-cell aluminum-foam core in three-point bending

In this paper, the response and failure of sandwich beams with aluminum-foam core are investigated. Quasi-static and low-velocity impact bending tests are carried out for sandwich beams with aluminum-foam core. The deformation and failure behavior is explored. It is found that the failure mode and the load history predicted by a modified Gibson's model agree well with the quasi-static experimental data. The failure modes and crash processes of beams under impact loading are similar to those under quasi-static loading, but the force-displacement history is very different. Hence the quasi-static model can also predict the initial dynamic failure modes of sandwich beams when the impact velocity is lower than 5 m/s.     

Effect of openings on the behaviour and strength of R/C beams in shear

The effects of introducing a transverse opening on the behaviour and strength of reinforced concrete beams under predominant shear are presented and discussed in this paper. On the basis of observed structural response, some guidelines are suggested to classify the opening as “large” or “small”. For small openings, two types of diagonal tension failure have been identified, and a method of design using the current codes of practice is proposed. The method is illustrated by a numerical example.     

Higher order composite beam theory built on Saint-Venant’s solution. Part-II: Built-in effects influence on the behavior of end-loaded cantilever beams

The higher order composite beam theory (HOCBT), established in Part-I, is a refinement of the one-dimensional beam-like theory related to 3D Saint-Venant’s solution. HOCBT is based on a displacement model including in/out-of plane warpings and is devoted to symmetric and orthotropic composite beams.     

Damage detection in beams from modal and wavelet analysis using a stationary roving mass and noise estimation

This paper uses the Continuous Wavelet Transform Analysis on mode shapes for damage identification. The wavelet analysis is applied to the difference in the mode shapes between a healthy and a damaged state. The paper also includes a novel methodology for estimating the level of noise of the experimental mode shapes based on a standard Signal to Noise Ratio (SNR). The estimated SNRs are used for identifying and making emphasis on the less noisy data. Moreover, a mass attached to the structure is considered to enhance the sensitivity of the structure to damage. Modal analysis is performed for different positions of the mass along the beam. The results obtained for all the positions of the mass are combined so an averaging process is implicitly applied. The paper presents the results from an experimental test of a cantilever steel beam with different severity levels of damage at the same location. The results show that the use of the attached mass reduces the effect of noise and increases the sensitivity to damage. Little damage can be identified with the proposed methodology even using a small number of sensors and only the first five bending modes.     

Coupling effects in bending, buckling and free vibration of generally laminated composite beams

A closed form expression to determine the effective flexural modulus of a laminated composite beam is developed and presented in this contribution. This effective flexural modulus is applied to the bending, buckling and free vibration response of generally laminated composite beams with various boundary supports. The expression was developed using the combination of the Euler–Bernoulli beam and classical lamination theory. In addition the results of an extensive finite element analysis are used to validate the analytical model. The comparison of the analytical results, the finite element results and the experimental results showed good correlation. It is also observed that coupling response is an important variable that must be included in the computation of the effective flexural stiffness of generally laminated beam.     

Investigation of the mechanical behavior and vibration characteristics of thin walled glass/carbon hybrid composite beams under a fixed-free boundary condition

In the present work, woven fabric glass laminate is modified by interplying high modulus carbon fabric layers for improving the stiffness to weight ratio to enable good performance in dynamic conditions. The glass, carbon, and hybrid of glass/carbon laminates were fabricated with two different stacking sequences by hand layup method and tested for evaluating the mechanical properties with considerable trials. The vibration characteristics of composite beams were experimentally studied by impulse excitation techniques under fixed-free boundary conditions. The stacking sequence of beams influences the mechanical properties and vibration characteristics. The modal response of tested samples are compared and discussed.     

Influence of statistical and constraint loss size effects on cleavage fracture toughness in the transition - A model based analysis

A database derived from tests on specimens with a large range of ligament (b) and thickness (B) dimensions was systematically analyzed to evaluate constraint loss and statistical size effects on cleavage fracture toughness. The objectives were to: (1) decouple size effects related to constraint loss, mediated by b and B, from those arising from statistical effects, primarily associated with B; and, (2) develop procedures to transfer toughness data to different conditions of constraint and B. The toughness database for a Shoreham pressure vessel steel plate, tested at a common set of conditions, was described in a companion paper. Quantification of constraint loss was based on an independently calibrated 3D finite-element critical stress-area, σ^∗-[K_Jm/K_Jc], model. The measured toughness data, K_Jm, were first adjusted using computed [K_Jm/K_Jc] constraint loss factors to the corresponding values for small scale yielding conditions, K_Jc=K_Jm/[K_Jm/K_Jc]. The K_Jc were then statistically adjusted to a K_Jr for a reference B_r = 25.4 mm. The B adjustment was based on a critically stressed volume criterion, modified to account for a minimum toughness, K_min, consistent with modest modifications of the ASTM E 1921 Standard procedure. The combined σ^∗-[K_Jm/K_Jc]-K_min adjustment procedure was applied to the Shoreham b − B database, producing a homogeneous population of K_Jr data, generally within the expected scatter. The analysis suggests that: (1) there may be a maximum B beyond which statistical size effects diminish, and (2) constraint loss in the three-point bend specimens begins at a relatively low deformation level. A corresponding analysis, based on a Weibull stress, σ_w-[K_Jm/K_Jc]-K_min, adjustment procedure, yielded similar, but somewhat less satisfactory, results. The optimized adjustment procedure was also applied to other K_Jm data for the Shoreham plate from this study, as well as a large database taken from the literature. The population of 489K_Jr data points, covering an enormous range of specimen sizes, geometries and test temperatures, was found to be consistent with the same master curve T₀ = −84 °C derived from the b − B database. Thus, calibrated micromechanical models can be used to treat size and geometry effects on K_Jm, facilitating using small specimens and data transfer to predict the fracture limits of structures.     

A unified approach for the static and dynamic analyses of intermediate debonding in FRP-strengthened reinforced concrete beams

A spectral method is proposed for solving static and dynamic problems in FRP-strengthened reinforced concrete beams in a unified way. In order to appropriately simulate the debonding failure a mechanical model considering nonlinear stress–strain relationships for concrete and steel is used. The FRP-to-concrete interface is modelled using a realistic bilinear local bond-slip law. Numerical results with the proposed model for the interfacial shear stress distribution and the load–displacement response are derived for beams statically tested. Using the same spectral model the influence of interfacial delaminations on the dynamic characteristics of the structures is studied. The feasibility of the proposed method for performing dynamic analyses for high frequency excitations in a very simple and non-expensive way makes this study very useful in non-destructive testing analyses as a tool for diagnoses and detection of debonding in its initial stage by monitoring the change in dynamic characteristics.     

Behavior and performance of RC T-section deep beams externally strengthened in shear with CFRP sheets

A series of experimental tests were carried out to investigate the behavior and performance of reinforced concrete (RC) T-section deep beams strengthened in shear with CFRP sheets. Key variables evaluated in this study were strengthening length, fiber direction combination of CFRP sheets, and an anchorage using U-wrapped CFRP sheets. A total of 14 RC T-section deep beams were designed to be deficient in shear with a shear span-to-effective depth ratio (a/d) of 1.22. Crack patterns and behavior of the tested deep beams were observed during four-point loading tests. Except the CS-FL-HP specimen, almost all strengthened deep beams showed a shear–compression failure due to partial delamination of the CFRP sheets. From the load–displacement (p–u) curves, the effects of key variables on the shear performance of the strengthened deep beams were addressed. It was concluded from the test results that the key variables of strengthening length, fiber direction combination, and anchorage have significant influence on the shear performance of strengthened deep beams. In addition, a series of comparative studies between the present experimental data and theoretical results in accordance with the commonly applied design codes were made to evaluate the shear strength of a control beam and deep beams strengthened with CFRP sheets.     

Influence of hydrostatic pressure on the mechanical behavior and properties of unidirectional, laminated, graphite-fiber/epoxy-matrix thick composites

This paper reviews and gives new insight into earlier work by the author and his co-workers on the experimental investigation of the influence of superimposed hydrostatic pressure on the mechanical behavior and properties of the epoxy used for the matrix and unidirectionally laminated, graphite-fiber/ epoxy-matrix thick composites. The direction of the fibers was, respectively, 0°, 45° and 90° for the compressive test samples and 0°, 45° -45° and 90° for the shear samples.

Hydrostatic pressure induces very significant, often dramatic changes in the compressive and shear stress/ strain behavior of composites, and consequently in the elastic, yielding, deformation and fracture properties. The range of pressures covered for the compressive experiments was 1 bar to 4 kbar, and for the shear tests 1 bar to 6 kbar. The shear modulus (G) of the epoxy increased bilinearly with pressure, with the break, or the discontinuity point, occurring at 2 kbar. The compressive elastic modulus (E) and the shear modulus (G) of the composites increase in the same manner as for the epoxy. The break, which is located at 2 kbar, represents a pressure at which physical changes in the molecular motion of the matrix epoxy occur. That is, segmental motion of molecules between the cross-links is frozen in by 2 kbar pressure. This pressure is known as the secondary glass transition pressure of the epoxy at room temperature. Alternatively, the sub-zero secondary glass transition temperature of the epoxy is shifted to ambient temperature by 2 kbar pressure. The increase in the moduli may also be given a mechanical interpretation. The elastic or shear modulus of an isotropic, elastic material due to small compressive or shear deformations, respectively, superimposed on a finite volume deformation, which is caused by hydrostatic pressure, increases with pressure. Such an increase in E or G has been predicted using finite deformation theory of elasticity.

The normally brittle epoxy develops yielding when the superimposed hydrostatic pressure exceeds 2 kbar. The shear yield stress (1% off-set) of the epoxy increases linearly with pressure above 2 kbar. This kind of yielding behavior can be predicted by a pressure-dependent yield criterion. The compressive yield strength of the 45° and 90° composites increases bilinearly with pressure, and the shear yield strength of the 0°, 45° and 90° composites also increases bilinearly with pressure. This bilinear behavior is also due to the secondary glass transition pressure of the matrix epoxy, being located at 2 kbar. The fracture strength of the composites also increases with pressure linearly and the greatest increase occurs in the 45° composite in compression and in the −45° composite in shear. The fracture modes of the composites undergo changes with increasing hydrostatic pressure. For instance, the 0° composite undergoes a brittle-ductile transition under shear stress, while no such transition appears to set in under compressive stress. The fracture mode of the 45° composite changes from matrix failure at lower pressures to fiber failure at high pressures under shear stress.     

Digital-sampling systems in high-resolution and wide dynamic-range energy measurements: Finite time window, baseline effects, and experimental tests

Fast digital sampling and signal processing of the output of charge-sensitive preamplifiers connected to solid-state detectors, used in nuclear physics experiments, constitute effective replacements of the standard analog methods. If high-resolution and high-speed sampling Analog to Digital Converters (ADCs) are used, both the energy and timing resolution performances of the detector can be effectively exploited. The choice of a particular fast ADC in these applications is strictly related to the desired resolution and dynamic range of the system. In this paper a quantitative evaluation of system resolution is carried out—the results of [L. Bardelli and G. Poggi, Digital sampling-systems in high-resolution and wide dynamic-range energy measurements: comparison with peak sensing ADCs, this issue] are extended taking into account not only the detector noise, the digitizer properties, and the digital shaping, but also the use of a finite time interval for both baseline evaluation and digital shaping. The resulting performances are expressed using the parameter PSENOB [L. Bardelli, G. Poggi, Digital sampling-systems in high-resolution and wide dynamic-range energy measurements: comparison with peak sensing ADCs, this issue] and two additional correction terms. The effects due to ADC non-linearities are also briefly addressed. Simulations are presented to validate the proposed recipe. Experimental tests using a germanium detector in a wide dynamic-range configuration (at different counting rates) as well as an application to ΔE-E charged particle identification are shown. The presented discussion and results can be directly extended to various experimental arrangements.     

On the modal behavior of a three-dimensional functionally graded cantilever beam: Poisson’s ratio and material sampling effects

Modal behavior of a three-dimensional (3D) homogeneous and functionally graded (FG) cantilever beam is studied using the Rayleigh–Ritz (RR) method and the finite element method (FEM). The effect of Poisson’s ratio and material sampling point on the natural frequencies is further addressed using the FEM. The natural frequencies (first three) obtained using the RR method converge as the number of admissible shape functions increase. The natural frequencies (first 15) obtained using the FEM vary considerably with the material gradation, more so for the lower modes than for the higher modes. Poisson’s ratio significantly changes the torsional natural frequencies of the homogeneous and graded beams. Considerable change in the natural frequencies is seen for the linear graded beams whose material properties are sampled at the element centroid rather than at Gaussian integration points. This difference is easily observed for beams modeled using a coarse mesh rather than a fine mesh. The natural frequencies of the y   direction hyperbolic tangent beam with material nonhomogeneity parameter β=100$\beta =100$ matches well with those of the y direction bi-material beam. The natural frequencies of the power-law graded 3D cantilever beam obtained using the FEM matches closely with the 2D reference (Qian and Ching, 2004 [1]) solution obtained using the meshless local Petrov–Galerkin method.