Large Structural Deformations Research Articles

Impact of GPS satellite and pseudolite geometry on structural deformation monitoring: analytical and empirical studies

Global positioning systems (GPS) have in recent years been increasingly used to monitor the deformations of large structures, particularly the deflections of long suspension bridges. When appropriately employed, and with the presence of a strong satellite geometry, GPS can supply timely and accurate structural deformation information. However, the three-dimensional (3-D) positioning accuracies in a local coordinate system are uneven. For instance, the vertical component of 3-D coordinates is less accurate than the horizontal component. In addition, GPS satellite availability tends to be a function of the latitude of the observation site and its surrounding obstructions. As a consequence, the accuracy of the north–south component is typically worse than that of the east–west component in mid-latitude areas (φ>45∘), and in some of the worst situations the horizontal positioning accuracy could even degrade to the same level as that of the vertical component. With such measurements it might not be possible to correctly interpret the real structural deformations. Furthermore, an insufficient number of satellites, caused by signal obstruction, could make it impossible to use GPS alone for kinematic positioning, even when integrated with other sensors such as triaxial accelerometers. With the aim of improving 3-D positioning accuracies for the monitoring of structural deflections, especially in vertical and northern directions, the optimal location selection of an array of ground-based pseudolites to augment GPS satellite geometry using an analytical simulation technique proposed by the authors is considered. Achievable 3-D positioning accuracies are estimated by simulating a real bridge deformation scenario using augmented transmitter geometry and compared with actual positioning accuracies calculated from the measurements gathered from a bridge trial. The results show that with an augmented satellite geometry and multipath mitigation it is possible to achieve uniform 3-D positioning accuracies of a few millimetres.

Simulation of swimming organisms: coupling internal mechanics with external fluid dynamics

Problems in biological fluid dynamics typically involve the interaction of an elastic structure with its surrounding fluid. A unified computational approach, based on an immersed boundary framework, couples the internal force-generating mechanisms of organisms and cells with an external, viscous, incompressible fluid. Computational simulation, in conjunction with laboratory experiment, can provide valuable insight into complex biological systems that involve the interaction of an elastic structure with a viscous, incompressible fluid. This biological fluid-dynamics setting presents several more challenges than those traditionally faced in computational fluid dynamics - specifically, dynamic flow situations dominate, and capturing time-dependent geometries with large structural deformations is necessary. In addition, the shape of the elastic structures is not preset: fluid dynamics determines it. This article presents our recent progress on coupling the internal molecular motor mechanisms of beating cilia and flagella with an external fluid, as well as the three-dimensional (3D) undulatory swimming of nematodes and leeches. We expect these computational models to provide a testbed for examining different theories of internal force-generation mechanisms.

Simulation of Train Crashes in Three Dimensions

Summary It is important to predict the crash behavior of trains to improve their crashworthiness. This paper investigates the simulation of high-speed train crashes in three dimensions using multibody dynamics. At present, little is known about three-dimensional crash simulations. This study shows that it is possible to simulate overriding, derailment and lateral buckling, including results from one-dimensional or two-dimensional simulations. Several factors, however, such as computational time and large deformation of structures, need further investigation.

Coupled seismic response analysis of rubble-mound breakwaters

The present investigation considers the seismic behaviour of rubble-mound breakwaters by taking into account the coupling between the hydrodynamic loading and the shaking of the mound. To this end a boundary element code was developed that predicts the hydrodynamic pressures on the faces of the breakwater. This was coupled with a geotechnical code providing the accelerations along the height of the structure. Shaking-table experiments were carried out to verify the model. The methodology was then applied to real-life structures. It is found that the quality of the foundation soil directly and decisively affects the pressures and induced accelerations. Weak foundations can trigger large structure deformations. In tall structures the pressures and accelerations of the mound increase with frequency. Far from resonance, the maximum pressures on the slopes occur at 40% of the water depth from the bed. The total hydrodynamic force can be high under resonance conditions. It is also found that Westergaard's expression overestimates pressures, except in cases of rigid base and shakings of small acceleration and high frequency. The coupling of the hydrodynamic loading and the shaking of the mound, as well as the frequency dependence of the model, represent advances over the conventional Westergaard's relation.

Coupled seismic response analysis of rubble-mound breakwaters

The present investigation considers the seismic behaviour of rubble-mound breakwaters by taking into account the coupling between the hydrodynamic loading and the shaking of the mound. To this end a boundary element code was developed that predicts the hydrodynamic pressures on the faces of the breakwater. This was coupled with a geotechnical code providing the accelerations along the height of the structure. Shaking-table experiments were carried out to verify the model. The methodology was then applied to real-life structures. It is found that the quality of the foundation soil directly and decisively affects the pressures and induced accelerations. Weak foundations can trigger large structure deformations. In tall structures the pressures and accelerations of the mound increase with frequency. Far from resonance, the maximum pressures on the slopes occur at 40% of the water depth from the bed. The total hydrodynamic force can be high under resonance conditions. It is also found that Westergaard's expression overestimates pressures, except in cases of rigid base and shakings of small acceleration and high frequency. The coupling of the hydrodynamic loading and the shaking of the mound, as well as the frequency dependence of the model, represent advances over the conventional Westergaard's relation.

Finite Element Simulation of a Full-Scale Crash Test of a Composite Helicopter

Finite Element Simulation of a Full-Scale Crash Test of a Composite Helicopter

Prediction of Butt Welding Deformation of Curved Shell Plates by Inherent Strain Method

In order to achieve high productivity of assembly blocks of hull structure, it is important to predict welding deformations accurately and to apply these data to the production planning. For this purpose the transient thermal-elastic-plastic analysis by FEM (finite-element method) may be utilized. However, this method is not a practical approach to analyze the deformation of large and complex structures, such as ship hull structures, in view of time and cost. Whereas the inherent strain method deals the residual strain near the weld line as the inherent strain, therefore the residual deformation can be simply calculated by elastic analysis. This method is much more practical and efficient than the transient thermal-elastic-plastic analysis. Thus, in this paper, the inherent strain method is used to predict the welding deformation of hull structures. Past research activities of the inherent strain method have been focused on the prediction of the welding deformation of small size specimens and simple shape specimens; however, very few of them treat the problem of large and complex structures. Hence, in this paper, prediction of welding deformation of curved shell plate, of which size is approximately full scale, is conducted by the inherent strain method. In applying elastic analysis to predict the welding deformation of actual hull blocks, contact condition between the plate and the positioning jig should be adequately realized in the analysis. Therefore, a practical solution is proposed to con- sider the contact condition between the plate and the jig by judging reaction forces of the jig at calculation steps. Furthermore, since the welded plates may slip on the positioning jig due to the welding deformation, rigid body motion of plates is caused. Hence this motion should be taken into account of the estimation of calculated results of FEM. In addition to the rigid body motion, coordinate system of the measured data is usually different from the calculated data, therefore, the deviation of the coordinate system must be involved. These calibrations to assess the calculated deformation by FEM are also discussed. The above prediction method is confirmed to be successful by comparing the calculated deformations and the measured ones of large size specimen of curved shell plates due to butt welding.

Computational studies of carbon nanotube structures

Here we continue our previous exploratory work [Huhtala et al., Comput. Phys. Commun. 146 (2002) 30] in investigating carbon nanotube structures under different bending strain conditions by using large-scale molecular dynamics simulations. On the one hand bending strain is obtained by forcing nanotubes of different chirality to a closed toroidal configuration and on the other hand by bending a straight nanotube along a semicircle. Our previous work has indicated that the toroidal form buckles at a critical radius without changes in the local hexagonal bonding structure when the temperature is relatively low. Here this work has been continued by studying buckled tori at very high temperatures, where bond breakages in the form of pentagon–heptagon pair creation have been observed. These thermally excited defects seem to settle mainly in the unbuckled regions of the torus. The buckling phenomenon was also found to take place when straight single-walled nanotubes were bent along a semicircle. For a small and moderate amount of bending buckling behaviour seems similar to that observed in nanotori while for large bendings large structural deformations of the tube are observed. These include bond breakages and rupture, being dependent on the chirality of the tube.

Pressure and Orientation Effects on the Electronic Structure of Carbon Nanotube Bundles

On the basis of the density functional theory, we study pressure and orientation effects on geometric and electronic structures of crystalline bundles consisting of single-wall carbon nanotubes, (6,0), (8,0), (6,6), and (12,0). We find that mutual orientation angles of adjacent nanotubes in stable geometries correspond to a common intertube atomic arrangement which is similar to an interlayer atomic arrangement of the graphite “AB stacking”. In the (6,6) bundle, it is found that a pseudogap appears at the Fermi level and its width depends strongly on the intertube orientation. Interestingly, this pesudogap becomes the widest at the most stable intertube orientation which in this case is slightly off the ideal AB-stacking geometry, indicating that the electronic energy gain enhances the pseudogap effect in metallic nanotube bundles. Under lateral pressure, large structural deformation (buckling) is found in the (6,6) bundle and the cross section of the tube in the bundle is deformed from circular to polygo...

A Practical Estimation Method of the Skin Plate Distortion Derived from Fillet Weld

The fabrication accuracy of ship building block must be improved in order to raise the degree of the automation of ship built-up stage. Many research projects concerning this problem have been carried out and some practical or precise methods to estimate the welding deformation have proposed. Equivalent inherent strain method, on which the inherent strain derived from thermal cycles of welding is considered as the generating source of deformation, is a convenient method to calculate the welding deformation of large welded built-up structures. However, this method does not give a good estimation result in case of generating the large deformation such as a distortion of skin plate.In this paper, the improvement of equivalent inherent strain method to raise the precision of the distortion derived from fillet weld is carried out. Beam element, which expresses the fillet weld bead and has inherent strain generating tendon force, is incorporated with the former equivalent inherent strain method. The experimental results, which welding deformation was measured, are compared with the calculation by applying the proposed method. As a result, the validity of the improvement is confirmed.

Geometrically Nonlinear Shell Element for Hygrothermorheologically Simple Linear Viscoelastic Composites

A triangular flat shell element for large deformation analysis of linear viscoelastic laminated composites is presented. Hygrothermorheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Recurrence relations are developed and implemented for the evaluation of the viscoelastic memory loads. The nonlinear deformation process is computed using an incremental/iterative approach with the Newton-Raphson Method used to find the incremental displacements in each step. The presented numerical examples consider the large deformation and stability of linear viscoelastic structures under deformation-independent mechanical loads, deformation-dependent pressure loads, and thermal loads. Unlike elastic structures that have a single critical load value associated with a given snapping of buckling instability phenomenon, viscoelastic structures will usually exhibit a particular instability for a range of applied loads over a range of critical times. Both creep buckling and snap-through examples are presented here. In some cases, viscoelastic results are also obtained using the quasielastic method in which load-history effects are ignored, and time-varying viscoelastic properties are simply used in a series of elastic problems. The presented numerical examples demonstrate the capability and accuracy of the formulation.

Gradient‐based refinement indicators in adaptive finite element analysis with special reference to sheet metal forming

Two mesh refinement indicators based on the gradients of effective stress (GSIG) and effective plastic strain (GEPS), respectively, are proposed for adaptive finite element analysis of the large deformation, quasi‐static or dynamic response of shell structures. The mesh refinement indicators are based on equi‐distributing the variation of stresses or plastic strains over the elements of the mesh. A program module is developed and implemented in the non‐linear explicit finite element code LS‐DYNA. This module provides element‐wise refinement evaluations so that selective mesh refinements are carried out in regions of the mesh where the values of local indicators exceed a user‐specified tolerance. The FE model of a conventional deep drawing process is used as a numerical model, including both material and geometrical non‐linearities, in order to demonstrate the versatility of the two refinement indicators. Four different refinement indicators, based on angle change, thickness change, GSIG and GEPS, are applied in this investigation. The numerical results are compared with experimental results regarding the thickness distribution versus cup height, cup height variation versus circumference angle, effective plastic strain in the deformed sheet and punch force. It is shown that the proposed indicators can identify finite elements which have high gradients of effective stress or effective plastic strain so that the mesh is refined in the regions undergoing the most severe deformations and the numerical results are improved.

Numerical simulations of large deformation of thin shell structures using meshfree methods

In this paper, meshfree simulations of large deformation of thin shell structures is presented. It has been shown that the window function based meshfree interpolants can be used to construct highly smoothed (high order “manifold”) shape functions for three-dimensional (3-D) meshfree discretization/interpolation, which can be used to simulate large deformation of thin shell structures while avoiding ill-conditioning as well as stiffening in numerical computations. The main advantage of such 3-D meshfree continuum approach is its simplicity in both formulation and implementation as compared to shell theory approach, or degenerated continuum approach. Moreover, it is believed that the accuracy of the computation may increase because of using 3-D exact formulation. Possible mechanism to relieve shear/volumetric locking due to the meshfree interpolation is discussed. Several examples have been computed by using a meshfree, explicit, total Lagrangian formulation. Towards to developing a self-contact algorithm, a novel meshfree contact algorithm is proposed in the end.

Nonlinear vibration analysis of geometrically nonlinear shell structures

The nonlinear vibration analysis of a geometrically nonlinear shell structure is investigated in this study. In general, when the shell structure is subjected to excessive loadings, the large deformation of the shell structures must be considered, and the governing equation of the shell structure becomes nonlinear since the stiffness matrix of the governing equation is related to the deflection. Therefore, the natural frequency of the shell structure is varied with respect to the time which is quite different from that of the linear structures. In order to solve the nonlinearity of the governing equations of the shell structures, the well known Newton-Raphson iteration procedure in conjunction with Newmark scheme is adopted to perform the frequency analysis of the nonlinear-shell structures. Incidentally, the natural frequencies for various curvatures of the shell structures are also investigated from the practical engineering point of view.

A Study on the Prediction of Deformations of Welded Ship Structures

Welding deformations injure the beauty of appearance of a structure and decrease its buckling strength. In addition, welding deformations cause errors during the assembly of the structure and prevent increase of productivity. Welding deformations of real structures are complicated and the accurate prediction of welding deformations has been a difficult problem. This study presents a method to predict welding deformations of large structures accurately and practically based on the accumulated research results. The presented method uses the finite element method combining the inherent strain theory and the experimental results for accurate and efficient analysis. The weld joint is assumed to be divided into 3 regions: inherent strain region, material softening region and base metal region. The simplified elasto-plastic analysis method is introduced and representative material values during the thermal elasto-plastic process are used in this method. It is revealed from the analysis results for the simple welded model that the inherent strains are changed by joint restraint as well as heat input and elastic modulus of the inherent strain region, and the material softening region must be different from that of the base metal region. These results have been supported by the experimental data. The method proposed in this study can be combined with the commercial finite element analysis software to predict reasonably an efficiently the welding deformations of large structures.

A Structural Nonlinear Analysis Workspace (SNAW) based on meshless methods

In this paper, a Structural Nonlinear Analysis Workspace (SNAW) based on meshless methods is presented. Using the meshless methods in SNAW, the modeling of structures for nonlinear analysis is accomplished by a set of particles, and the use of an explicit structured mesh as in the conventional finite element methods is unnecessary. Due to the use of smooth shape functions in the meshless methods, SNAW effectively deals with large structural deformations that usually lead to mesh distortion and solution divergence in finite elements. The meshless formulation in SNAW is applicable to hyperelastic and elasto-plastic materials, explicit and implicit time integrations, and rigid-to-flexible-body frictional contact conditions. This SNAW development interfaces meshless analysis code with MSC/PATRAN for pre- and post-processing using graphical menu-driven functionalities. A number of example problems, including engine mount, rubber seal, metal bar impact and metal-forming simulations, are presented to demonstrate the effectiveness of SNAW.

Sensitivity and optimisation procedures for truss structures under large displacement

The work presented here focuses on the development of suitable discretised formulations, for large-displacement shape and non-shape design sensitivity analysis (DSA), which enable the straightforward incorporation of structural optimisation into established finite element analysis (FEA) codes. For the generalised displacement-based functional the design sensitivity vector has been expressed in terms of displacement sensitivity. The Total Lagrangian formulation is utilised for modelling of large deformation of truss structures. The variational formulation of the sensitivity analysis procedure is discretised by using pseudo - finite elements, Results are presented for the sensitivity analysis and optimisation of standard truss structures. For the purposes of this work, the analysis and optimisation procedures outlined below are incorporated into the FEA code ABAQUS.

A Multibody/Finite Element Analysis Approach for Modeling of Crash Dynamic Responses

Computer models of the human body are robust tools for gaining insight into the gross motion of ground vehicle or aircraft occupants and evaluating the loads and, deformations of their critical parts. The knowledge of occupant responses will help in the determination of the type and probable causes of injuries that may he sustained during a crash. An important aspect in crash analysis is how the large motion of the relatively rigid segments of an occupant, such as the limbs, and the small deformations of flexible segments, such as the spine column, are interrelated. To this end, a general methodology for kineto-static analysis of multibody systems with flexible structures undergoing large motion and structural deformations is developed. Rigid multibody dynamics is used to predict the gross motions and displacements at the boundaries between the relatively bulky (rigid) bodies and relatively flexible ones. A mixed boundary-condition finite-element analysis is formulated and solved at every numerical integration time to determine the corresponding reaction forces and moments at the boundaries and also the structural deformations. Based on this methodology, a multibody model of the occupant with a nonlinear finite element model of the lumbar spine is developed for a Hybrid II anthropomorphic crash test dummy. The analytical results obtained are compared with the experimental results from the impact sled tests. Comparison of the results has shown better correlation between the analyses and the experiments compared with earlier studies.

Large-deformation analysis of flexible beams

Presented here are numerical verifications of a geometrically-exact curved beam model which fully accounts for large rotations, large displacements, initial curvatures and extensionality. A multiple shooting method is used to solve the two-point boundary-value problem of flexible beams undergoing large elastic rotations and displacements in three-dimensional space. Numerically exact large static deformations of eight beams subjected to different loading and/or boundary conditions are obtained. These solutions can be used to verify the performance of general finite-element codes in analyzing large structural deformations.

Photophysics and photochemistry of sterically strained α-haloanthraquinones: The bromo and/or chloro substituted compounds

The steric hindrance between the oxygen and halogen atoms results in the structural deformation of α-haloanthraquinones and their lowest excited triplet (T 1 ) states are of mixed nπ*-ππ* or ππ* character with unusually short lifetimes. Moreover, the rates of hydrogen-atom abstraction from ethanol by the T, states decrease with their increasing ππ* character, and the proximity of the halogen atom to the hydroxy group causes the photochemical intramolecular elimination of hydrogen halide from the initial photoproducts (α-haloanthrahydroquinones) yielding α-haloanthraquinones (or anthraquinone) with one less halogen atom than the original molecule; the final product is anthrahydroquinone. The remarkably large structural deformation of 1,8-dihaloanthraquinones, furthermore, makes it possible to observe an absorption band due to a complex of two 1,8-dihaloanthrasemiquinone radicals which gives rise to the simultaneous formation of 1,8-dihaloanthrahydroquinones and the original anthraquinones. Of particular interest is observation of the absorption band(s) attributable to the second excited triplet (T 2 ) states of 1,8-dihaloanthraquinones. However, the electron transfer from triethylamine (TEA) to these T 2 states generating the radical anions is observed only in acetonitrile, while that to the T 1 states generating their exciplexes with TEA is observed not only in acetonitrile but also in toluene and ethanol.