Theoretical Prediction of the Bending Stiffness of Reinforced Thermoplastic Pipes Using a Homogenization Method

The accurate prediction of bending stiffness is important to analyze the buckling and vibration behavior of reinforced thermoplastic pipes(RTPs)in practical ocean engineering.In this study,a theoretical method in which the constitutive relationships between orthotropic and isotropic materials are unified under the global cylindrical coordinate system is proposed to predict the bending stiffness of RTPs.Then,the homogenization assumption is used to replace the multilayered cross-sections of RTPs with homogenized ones.Different from present studies,the pure bending case of homogenized RTPs is analyzed,considering homogenized RTPs as hollow cylindrical beams instead of using the stress functions proposed by Lekhnitskii.Therefore,the bending stiffness of RTPs can be determined by solving the homogenized axial elastic moduli and moment of inertia of cross sections.Compared with the existing theoretical method,the homogenization method is more practical,universal,and computationally stable.Meanwhile,the pure bending case of RTPs was simulated to verify the homogenization method via conducting ABAQUS Explicit quasi-static analyses.Compared with the numerical and existing theoretical methods,the homogenization method more accurately predicts the bending stiffness and stress field.The stress field of RTPs and the effect of winding angles are also discussed.

A Finite Element Cable Model and Its Applications Based on the Cubic Spline Curve

For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables.

Static analysis of ultra-thin beams based on a semi-continuum model

A linear semi-continuum model with discrete atomic layers in the thickness direction was developed to investigate the bending behaviors of ultra-thin beams with nanoscale thickness.The theoretical results show that the deflection of an ultra-thin beam may be enhanced or reduced due to different relaxation coefficients.If the relaxation coefficient is greater/less than one,the deflection of micro/nano-scale structures is enhanced/reduced in comparison with macro-scale structures.So,two opposite types of size-dependent behaviors are observed and they are mainly caused by the relaxation coefficients.Comparisons with the classical continuum model,exact nonlocal stress model and finite element model （FEM） verify the validity of the present semi-continuum model.In particular,an explanation is proposed in the debate whether the bending stiffness of a micro/nano-scale beam should be greater or weaker as compared with the macro-scale structures.The characteristics of bending stiffness are proved to be associated with the relaxation coefficients.

Prediction on Deflection of Inflated Beam

The bending stiffness of the inflated beam is considered as a constant before wrinkles appear, and it decreases obviously as wrinkles propagate. The formula of the bending stiffness is obtained based on the membrane theory in this paper. Furthermore, the definition of dimensionless bending stiffness factor is presented; the relationship of bending stiffness factor and wrinkling factor is derived; the bending stiffness factor is simplified as different linear functions with wrinkling factor, and the simplified model of bending stiffness of inflated beam under bending is also obtained. The bending stiffness including expression of wrinkling factor is substituted into the deflection differential equation, and then the slope and deflection equation of the inflated beam is deduced by integrating the deflection differential equation. Finally, the load-deflection curve is obtained, which is compared with the experimental data in a previous paper. It has a good agreement with each other.

Nonlinear elastic constitutive relations of residually stressed composites with stiff curved fibres

Mechanical models of residually stressed fibre-reinforced solids,which do not resist bending,have been developed in the literature.However,in some residually stressed fibre-reinforced elastic solids,resistance to fibre bending is significant,and the mechanical behavior of such solids should be investigated.Hence,in this paper,we model the mechanical aspect of residually stressed elastic solids with bending stiffness due to fibre curvature,which up to the authors’knowledge has not been mechanically modeled in the past.The proposed constitutive equation involves a nonsymmetric stress and a couple-stress tensor.Spectral invariants are used in the constitutive equation,where each spectral invariant has an intelligible physical meaning,and hence they are useful in experiment and analysis.A prototype strain energy function is proposed.Moreover,we use this prototype to give results for some cylindrical boundary value problems.

Damage Detection for Simply Supported Bridge with Bending Fuzzy Stiffness Consideration

The benchmark of a simply supported beam with damage and bending fuzzy stiffness consideration is established to be utilized for damage detection. The explicit expression describing the Rotational Angle Influence Lines(RAIL) of the arbitrary section in the benchmark is presented as the nonlinear relation between the moving load and the RAIL appeared, when the moving load is located on the damage area. The damage detection method is derived based on the Difference of the RAIL Curvature(DRAIL-C) prior to and following arbitrarily section damage in a simply supported beam with bending fuzzy stiffness consideration. The results demonstrate that the damage position can be located by the DRAIL-C graph and the damage extent can be calculated by the DRAIL-C curve peak. The simply supported box girder as a one-dimensional model and the simply supported truss bridge as a three-dimensional model with the bending fuzzy stiffness are simulated for the validity of the proposed method to be verified. The measuring point position and noise intensity effects are discussed in the simply supported box girder example. This paper provides a new consideration and technique for the damage detection of a simply supported bridge with bending fuzzy stiffness consideration.

A novel structural modification to eliminate the early coupling between bending and torsional mode shapes in a cable stayed bridge

In this paper, a novel structural modification approach has been adopted to eliminate the early coupling between the bending and torsional mode shapes of vibrations for a cable stayed bridge model generated using ABAQUS software. Two lateral steel beams are added to the middle span of the structure. Frequency analysis is dedicated to obtain the natural frequencies of the first eight mode shapes of vibrations before and after the structural modification approach. Numerical simulations of wind excitations are conducted for the 3D model of the cable stayed bridge with duration of 30 s supporting on real data of a strong wind from the literature. Both vertical and torsional displacements are calculated at the mid span of the deck to analyze both the bending and the torsional stiffness of the system before and after the structural modification. The results of the frequency analysis after applying lateral steel beams declared a safer structure against vertical and torsional vibrations and rarely expected flutter wind speed. Furthermore, the coupling between the vertical and torsional mode shapes has been removed to larger natural frequencies magnitudes with a high factor of safety. The novel structural approach manifested great efficiency in increasing vertical and torsional stiffness of the structure.

Bending and vibration of a discontinuous beam with a curvic coupling under different axial forces

The transverse stiffness and vibration characteristics of discontinuous beams can significantly differ from those of continuous beams given that an abrupt change in stiffness may occur at the interface of the former.In this study,the equations for the deflection curve and vibration frequencies of a simply supported discontinuous beam under axial loads are derived analytically on the basis of boundary,continuity,and deformation compatibility conditions by using equivalent spring models.The equation for the deflection curve is solved using undetermined coefficient methods.The normal function of the transverse vibration equation is obtained by separating variables.The differential equations for the beam that consider moments of inertia,shearing effects,and gyroscopic moments are investigated using the transfer matrix method.The deflection and vibration frequencies of the discontinuous beam are studied under different axial loads and connection spring stiffness.Results show that deflection decreases and vibration frequencies increase exponentially with increasing connection spring stiffness.Moreover,both variables remain steady when connection spring stiffness reaches a considerable value.Lastly,an experimental study is conducted to investigate the vibration characteristics of a discontinuous beam with a curvic coupling,and the results exhibit a good match with the proposed model.

Functional Morphology and Bending Characteristics of the Honeybee Forewing

The present work aimed to reveal the functional morphology and bending characteristics of the worker honeybee （Apis mellifera） forewing. Honeybee wings including the forewing and hindwing, which are mainly composed of veins and membranes, are a kind of typical hierarchical biomaterials. We investigated the cross-sections of membranes, veins and wing hairs through Scanning Electron Microscopy （SEM）. Based on the microscopic observation, it was found that the vein is a thick-walled cylinder, and the membrane possesses multilayered structure and so does the wing hair which shows the thread surface. At the vein-membrane conjunctive position, membranes and veins are assembled seamlessly and veins are packed smoothly and tightly by membranes into a whole, allowing honeybees to perform excellent flapping flight. In such a case, we also conducted the cantilevered bending experiment of honeybee forewing to explore their bending characteristics using a MTS Tytron 250 micro force tester. Experiment results indicate that the anti-bending capacity of the forewing along the spanwise direction is higher than that along the chordwise direction which is partly caused by the wing corrugation along the wing span detected by the micro-Computed Tomography （micro-CT）, and ventral load bearing ability is better than dorsal one along the spanwise and chordwise direction of the wing which is due to the stress-stiffening of membranes. It could be concluded that the structural configuration of the wing is closely relevant to wing biomechanical behaviors. All results above would provide a significant support for the design of bioinspired wings for Flapping Micro Aerial Vehicles （FMAV）.

Analytical and numerical analysis on the torsional performance of elliptically deformed tunnels in the longitudinal direction

Segmental lining structures constructed by shields/tunnel boring machines are often subjected to uneven longitudinal cross-section torsion as a result of eccentric external loads,which is extremely adverse to tunnel safety but has not received sufficient attention for a long time.To figure out the torsional performance of segmental tunnels,it is essential to assess the longitudinal torsional stiffness and active-torsion-rejection capability of a segmented tunnel.The aim of the paper is to derive an analytical solution to the longitudinal torsional stiffness of a segmental tunnel with existing elliptical deformation.The longitudinal torsional stiffness under different internal force combinations is deduced considering the longitudinal axial force and bending moment based on the equivalent continuous model and force balance equation.The validity of the analytical solution is verified by comparing it with finite element method results.Then,a parametric analysis,using the new analytical solution,is included to investigate the effect of the key parameters on torsional behaviors,including the segment size,the bolt size and the transverse bending stiffness,etc.It is found that:(1)the longitudinal torsional stiffness efficiency(LTSE)of the segmental tunnel decreases with the rise of segment thickness to diameter ratio but increases with the ring width to diameter ratio;(2)the LTSE reduces with the increase of the effective shear length but rises with the diameter of bolts;(3)the LTSE increases rapidly with the ratio of compression-torsion or bending-torsion.Furthermore,the envelope curve of the critical load(N0,M0)for a tunnel to actively resist a certain internal torque is given.The proposed solution can be easily utilized to determine the longitudinal torsional stiffness of segmental tunnels and is an effective tool for tunnel design and maintenance.

Mortarless structures based on topological interlocking

We review the principle of topological interlocking and analyze the properties of the mortarless structures whose design is based on this principle.We concentrate on structures built of osteomorphic blocks-the blocks possessing specially engineered contact surfaces allowing assembling various 2D and 3D structures.These structures are easy to build and can be made demountable.They are flexible,resistant to macroscopic fractures and tolerant to missing blocks.The blocks are kept in place without keys or connectors that are the weakest elements of the conventional interlocking structures.The overall structural integrity of these structures depends on the force imposed by peripheral constraint.The peripheral constraint can be provided in various ways:by an external flame or features of site topography,intemal prestressed cables/tendons,or self-weight and is a necessary auxiliary element of the structure.The constraining force also determines the degree of delamination developing between the blocks due to bending and thus controls the overall flexibility of the structure thus becoming a new design parameter.

Deflection analysis of reinforced concrete beams strengthened with carbon fibre reinforced polymer under long-term load action

This paper presents the results of an experimental research on reinforced concrete beams strengthened with an external carbon fibre reinforced polymer(CFRP) layer under long-term load action that lasted for 330 d.We describe the characteristics of deflection development of the beams strengthened with different additional anchorages of the external carbon fibre composite layer during the period of interest.The conducted experiments showed that the additional anchorage influences the slip of the external layer with respect to the strengthened element.Thus,concrete and carbon fibre composite interface stiffness decreases with a long-term load action.Therefore,the proposed method of analysis based on the built-up-bars theory can be used to estimate concrete and carbon fibre composite interface stiffness in the case of long-term load.