Strain Energy Of Structure Research Articles

Imogolite-like nanotubes: structure, stability, electronic and mechanical properties of the phosphorous and arsenic derivatives

Imogolite is a single-walled aluminosilicate nanotube (NT) found in nature that can be easily synthesized, as well as its analogue aluminogermanate NT. Based on geometrical assumptions and pKa values, species such as H3PO4, H3PO3, H3AsO3, H3AsO4 could also be candidates to form imogolite-like structures. In the present work, we provide insights about the stability, electronic, structural and mechanical properties of possible imogolite like NTs by means of self-consistent charge density-functional tight-binding method (SCC-DFTB). Similarly to aluminogermanate, where the tetrahedral silicate groups are replaced by germanate, in this work tetrahedral silicate groups are substituted by phosphate, phosphite, arsenate and arsenite units in the imogolite structure. Detailed analysis is focused on structural properties, strain energy, band gap and Mulliken charges distribution. The calculated strain energy curves for all studied zigzag imogolite-like NTs present well-defined minima, which change as a consequence of composition variation. Moreover, the strain energy curves of armchair imogolite-like NTs also present minima, although in all cases less stable than zigzags by at least 2.2 meV per atom. The insulating NT behaviour changes after internal modification from silicate to phosphate, phosphite, arsenate and arsenite, as well as the charge distribution inside and outside the nanotubes.

Wind-Induced Response and Equivalent Static Wind Loads of Long Span Roofs

Long span space roofs are characterized as multimode wind-induced response. Participation factors on the basis of the structural strain energy are defined to select dominant eigenmodes in the background response and dominant vibration modes in the resonant response. These dominant eigenmodes and dominant vibration modes are chosen as fundamental vectors to evaluate the universal equivalent static wind loads (ESWL) that would simultaneously reproduce multiple largest load effects. A least-squares approximation method is employed to calculate the combination factors of these fundamental vectors. The proposed method is then employed to study wind-induced response and universal ESWL of the Beijing National Stadium. The results show that the background response is much higher than the mean response and the resonant response; low-order eigenmodes and vibration modes have the most important contribution to the wind-induced response; the structural response at selected nodes and selected supports under the universal ESWL agrees well with actual dynamic peak response.

Correlation-Based Damage Detection for Complicated Truss Bridges Using Multi-Layer Genetic Algorithm

The study presents a multi-layer genetic algorithm (GA) approach using correlation-based methods to facilitate damage determination for through-truss bridge structures. To begin, the structure's damage-suspicious elements are divided into several groups. In the first GA layer, the damage is initially optimised for all groups using correlation objective function. In the second layer, the groups are combined to larger groups and the optimisation starts over at the normalised point of the first layer result. Then the identification process repeats until reaching the final layer where one group includes all structural elements and only minor optimisations are required to fine tune the final result. Several damage scenarios on a complicated through-truss bridge example are nominated to address the proposed approach's effectiveness. Structural modal strain energy has been employed as the variable vector in the correlation function for damage determination. Simulations and comparison with the traditional single-layer optimisation shows that the proposed approach is efficient and feasible for complicated truss bridge structures when the measurement noise is taken into account.

平面ラチス梁の終局耐震性能に及ぼす静的安全率の効果

Earthquake input energies have been discussed in considering seismic resistant capacities of structures. In the literature, it had been pointed out by the author et al. that potential energies due to self-weight and dead loads would be necessary to be taken into account in order to estimate the seismic resistance capacity in a good accuracy especially for beam type structures. The author presented an estimation method of ultimate seismic resistance capacity with the static absorbed energies considering potential energies. The method presented utilizes the two strain energies at an initial yield and a limit state, and a pseudo velocity response spectrum of seismic waves. Although it is based on an extrapolation method, it shows a good accuracy in the estimation of maximum input acceleration of seismic waves. The method includes a modification equation to improve the accuracy, considering the properties of elastic and plastic strain energies of structures during a pushover analysis. Then in this paper, the effect of static safety factors is investigated to make clear the meanings of coefficient in the modification equation, for lattice beams of two types, cross web type and warren type. As the results, a further modified estimation method is presented to predict the dynamic collapse level under excessive seismic motions with the information of pushover and free vibration analyses.

Structural damage identification based on Bayesian theory and improved immune genetic algorithm

In order to solve structural multi-damage identification problem, a two-stage damage detection method based on Bayesian theory and immune genetic algorithm (IGA) is presented. First, structural modal strain energy and frequency are considered as two kinds of information sources, and Bayesian theory is utilized to integrate the two information sources and preliminarily identify structural damage locations. After the damaged locations are determined, immune genetic algorithm is used to identify structural damage extent. Considering the search efficiency of the simple IGA is still not very good, some improved strategies are presented, such as culture vaccine, concentration control of the best antibody, and two termination conditions etc. Simulation results show that the two-stage method can precisely identify structural damage locations and extent, and the calculated results of the proposed improved IGA are obviously better than those of both the simple IGA and the genetic algorithm with elitist strategy.

Theoretical Proof for the Relationship between Cable-Strut Structures’ Stiffness and Prestress

From the point of strain energy, an important conclusion has been derived and proved that cable-strut structure stiffness will be enhanced with the increase of prestress, provided that the cable-strut structure is within the scope of linear elasticity, and external loads' work will be completely absorbed and transformed into structural strain energy.

Topology Tailoring Method of TWB Autobody Parts Based on HyperWorks

In the paper, a lightweight design method for tailor-welded blanks (TWBs), termed as Topology Tailoring Method (TTM), is proposed, which is based on topology optimization philosophy and in which the variable density method is employed so as to reach the goal of the smallest structure strain energy. By using this method, a TWB autodoor subjected to a specific working condition is topologically optimized in HyperWorks, thus obtaining the more lightweight autodoor. At last, a side impact simulation of the autodoor is demonstrated, thus showing the effectiveness of the method.

Multi-Object Resonant Response Equivalent Static Wind Load of Large-Span Roofs

According to the strain energy equivalent, the resonant response equivalent static wind load of large span roof is derived. It solves the matter that should consider numerous structural response control objects on calculating equivalent static wind load for large span roofs, and establishes relationship with the structural strain energy introduced by fluctuant wind loads. Finally, the method is used to resonant equivalent static wind load analysis of 2008 Beijing Olympic Tennis Center Stadium roof structure. The results illustrate that the method proposed in this paper is effective and the precision is reliable.

Background Response Equivalent Static Wind Load of Large-Span Roofs Based on Energy Equation

Based on strain energy equivalent, the background response equivalent static wind load of large span roof is derived. It solves the matter that should consider numerous structural response control objects on calculating equivalent static wind load of large span roofs, and establishes relationship with the structural strain energy introduced by fluctuant wind loads. Finally, the method is used to background equivalent static wind load analysis of China National Stadium roof structure. The results illustrate that the method proposed in this paper is effective and the precision is reliable.

Structural Damage Detection Based on Strain Energy and Evidence Theory

In order to solve the damage detection problem, a damage detection method based on strain energy and evidence theory is presented in this paper. First, an evidence theory method is proposed to identify structural damage locations. Then, structural modal strain energy is utilized to quantify structural damage extents. In general, structural strain energy dissipation should be equal to the change of modal strain energy, according to this theory, a new energy equation is deduced, and structural damage extent can be obtained through the solution of the equation. The simulation results show that the method can perfectly identify damage locations and extents. Therefore, the proposed method is effective for the structural damage identification.

A structural constitutive model considering angular dispersion and waviness of collagen fibres of rabbit facial veins

BackgroundStructural constitutive models of vascular wall integrate information on composition and structural arrangements of tissue. In blood vessels, collagen fibres are arranged in coiled and wavy bundles and the individual collagen fibres have a deviation from their mean orientation. A complete structural constitutive model for vascular wall should incorporate both waviness and orientational distribution of fibres. We have previously developed a model, for passive properties of vascular wall, which considers the waviness of collagen fibres. However, to our knowledge there is no structural model of vascular wall which integrates both these features.MethodsIn this study, we have suggested a structural strain energy function that incorporates not only the waviness but also the angular dispersion of fibres. We studied the effect of parameters related to the orientational distribution on macro-mechanical behaviour of tissue during inflation-extension tests. The model was further applied on experimental data from rabbit facial veins.ResultsOur parametric study showed that the model is less sensitive to the orientational dispersion when fibres are mainly oriented circumferentially. The macro-mechanical response is less sensitive to changes in the mean orientation when fibres are more dispersed. The model accurately fitted the experimental data of veins, while not improving the quality of the fit compared to the model without dispersion. Our results showed that the orientational dispersion of collagen fibres could be compensated by a less abrupt and shifted to higher strain collagen engagement pattern. This should be considered when the model is fitted to experimental data and model parameters are used to study structural modifications of collagen fibre network in physiology and disease.ConclusionsThe presented model incorporates structural features related to waviness and orientational distribution of collagen fibres and thus offers possibilities to better understand the relation between structure and function in the vascular wall. Also, the model can be used to further study mechanically induced collagen remodelling in vascular tissue in health and disease.

Torsional strain energy evolution of carbon nanotubes and their stability with encapsulated helical copper nanowires

Torsional strain energy evolution of a single-walled carbon nanotube (CNT) and torsional stability of a CNT encapsulating a helical copper nanowire are investigated by molecular dynamics simulations. The strain energy transfer of the pristine CNT reveals a unique wave-like mode along the torsional axis and afterwards isoenergetic strips form helical distributions in the vicinity of the critical point. Ripples appear together with structural buckling and strain energy release at the buckling point. Although the insertion of a copper nanowire impedes abrupt structural buckling and increases the stability of the CNT, the increase depends greatly on the number of the metal atoms. This kind of hybrid would increase the critical torsional angle and the maximum torque of the corresponding CNT in the future application of nano-mechanical devices.

Optimization Design of Earthquake-Resistant Structure Taking Discrete Variables into Account

Conventionally, when optimizing a structure, the single target structural optimization design method is usually used. However, this design result often can not meet with the multiple requirements of construction; furthermore its optimizing efficiency is low; so its application is limited. And more, as the objective function being generally continuous variable, the optimized result is not the structural module and this is inconvenient for construction. This paper, taking the structural strain energy and the cost of construction as the targets to be optimized, and the design variable being discrete, provides multiple-target earthquake-resistant optimization design method aiming at obtaining the largest stain energy and the lowest construction cost, and established the function relation formula between the strain energy and the cost of construction and obtained the satisfied result. The highlight of this process is adopting discrete variables as the design variables, therefore the optimized results (cross-sectional dimensions) will conform to the requirements of structural module and the engineering practice. The optimization process presented in this paper conforms entirely to the national standards: “Code for Design of Reinforced Concrete Structures” (GB50010-2002) and “Code for Earthquake-resistant Design of Buildings” (GB50011). The theory and methods presented in this paper will be helpful for the structural design engineers and the researchers.

Combined Shape and Topology Optimization of Free Form Shells

With the aim of finding the optimum design that maximizes the stiffness of shell structures, an suitable approach for combined shape and topology optimization of free-form surface is presented. For numerical expression for the configuration of free form shell, NURBS (Non Uniform Rational B-Spline) is utilized. For shape optimization, the approach is employed to calculate the differential of total structural strain energy corresponding to surface height parameters. The surface height is adjusted iteratively according to its sensitivity to total structural strain energy. For topology optimization, the OC algorithms which are derived from the necessary optimality conditions are used and element connectivity is taken as design variable. The method has been implemented into a computational 3D model and example is provided to show the applicability of the present method.

A general formulation of structural topology optimization for maximizing structural stiffness

This paper presents a general formulation of structural topology optimization for maximizing structure stiffness with mixed boundary conditions, i.e. with both external forces and prescribed non-zero displacement. In such formulation, the objective function is equal to work done by the given external forces minus work done by the reaction forces on prescribed non-zero displacement. When only one type of boundary condition is specified, it degenerates to the formulation of minimum structural compliance design (with external force) and maximum structural strain energy design (with prescribed non-zero displacement). However, regardless of boundary condition types, the sensitivity of such objective function with respect to artificial element density is always proportional to the negative of average strain energy density. We show that this formulation provides optimum design for both discrete and continuum structures.

Role of elastin anisotropy in structural strain energy functions of arterial tissue

The vascular wall exhibits nonlinear anisotropic mechanical properties. The identification of a strain energy function (SEF) is the preferred method to describe its complex nonlinear elastic properties. Earlier constituent-based SEF models, where elastin is modeled as an isotropic material, failed in describing accurately the tissue response to inflation-extension loading. We hypothesized that these shortcomings are partly due to unaccounted anisotropic properties of elastin. We performed inflation-extension tests on common carotid of rabbits before and after enzymatic degradation of elastin and applied constituent-based SEFs, with both an isotropic and an anisotropic elastin part, on the experimental data. We used transmission electron microscopy (TEM) and serial block-face scanning electron microscopy (SBFSEM) to provide direct structural evidence of the assumed anisotropy. In intact arteries, the SEF including anisotropic elastin with one family of fibers in the circumferential direction fitted better the inflation-extension data than the isotropic SEF. This was supported by TEM and SBFSEM imaging, which showed interlamellar elastin fibers in the circumferential direction. In elastin-degraded arteries, both SEFs succeeded equally well in predicting anisotropic wall behavior. In elastase-treated arteries fitted with the anisotropic SEF for elastin, collagen engaged later than in intact arteries. We conclude that constituent-based models with an anisotropic elastin part characterize more accurately the mechanical properties of the arterial wall when compared to models with simply an isotropic elastin. Microstructural imaging based on electron microscopy techniques provided evidence for elastin anisotropy. Finally, the model suggests a later and less abrupt collagen engagement after elastase treatment.

Structural, Electronic, and Mechanical Properties of Single-Walled Halloysite Nanotube Models

Halloysite is a clay mineral with stoichiometry Al2Si2O5(OH)4·nH2O that can grow into long tubules and is chemically similar to kaolinite. In this work we present a systematic study on the stability, electronic, and mechanical properties of zigzag and armchair single-walled halloysite nanotubes by means of the self-consistent charge density-functional tight-binding method (SCC-DFTB). The detailed analysis is focused on structural properties, strain energy, and band gap as a function of tube radii and Mulliken charge distribution. The strain energy of halloysite nanotubes does not have a monotonic character and the most stable structures should be observed in the region of radii above 24 Å, in agreement with experimental data. Analysis of the electronic density of states shows that all tubes are insulators. Our calculations predict that single-walled halloysite nanotubes have Young modulus in the same order of imogolite and inorganic nanotubes, but smaller than that of carbon nanotubes. Even though most of the properties are adequately described by simpler halloysite models, further studies on multiwalled and larger diameter tubes are in progress.

1115 転位構造の弾性ひずみエネルギ評価に関する場の理論的研究(OS11. 材料の組織・強度に関するマルチスケールアナリシス(3),オーガナイズドセッション講演)

1115 転位構造の弾性ひずみエネルギ評価に関する場の理論的研究(OS11. 材料の組織・強度に関するマルチスケールアナリシス(3),オーガナイズドセッション講演)

Elastoplastic phase-field simulation of self- and plastic accommodations in [formula omitted] martensitic transformation

An elastoplastic phase-field (PF) model of martensitic transformation is proposed to study the effects of self- and plastic accommodations on the evolution of a stress-accommodating martensitic structure and elastic strain energy minimization. Cubic → tetragonal martensitic transformation in elastic and elastoplastic materials is simulated using our elastoplastic PF model. The PF model can predict the self- and plastic accommodation behaviors during the martensitic transformation, which relax the transformation-induced stress field. Therefore, it can be shown that the elastic strain energy associated with the transformation is largely reduced by both accommodations. Our PF simulation also indicates that plastic deformation in the matrix arrests the growth of the tetragonal martensite phase, as suggested by some theoretical and experimental studies. In the evolution of the martensitic microstructure with both self- and plastic accommodations, we can find that the delay of the formation of the self-accommodating variant takes place, because the transformation-induced stress field is considerably relaxed by plastic deformation before self-accommodation. Furthermore, we can confirm that plastic accommodation largely reduces the elastic strain energy during the formation of the tetragonal phase that is affected by both self- and plastic accommodations, such as lath martensite formation, by the proposed PF model.

Structural strain energy function applied to the ageing of the human aorta

Stiffening of the aorta with progressing age leads to decrease of aortic compliance and thus to an increase of pulse pressure amplitude. Using a strain energy function (SEF) which takes into account the composition of the arterial wall, we have studied the evolution of key structural components of the human thoracic aorta using data obtained from the literature. The SEF takes into account the wavy nature of collagen, which upon gradual inflation of the blood vessel is assumed to straighten out and become engaged in bearing load. The engagement of the individual fibers is assumed to be distributed log-logistically. The use of a SEF enables the consideration of axial stretch ( λ z ) and residual strain (opening angle) in the biomechanical analysis. Both λ z and opening angle are known to change with age. Results obtained from applying the SEF to the measurements of aortic pressure–diameter curves indicate that the changes in aortic biomechanics with progressing age are not to be sought in the elastic constants of elastin and collagen or their volume fractions of the aortic wall but moreover in alterations of the collagen mesh arrangement and the waviness of the collagen fibers. In old subjects, the collagen fiber ensemble engages in load bearing much more abruptly than in young subjects. Reasons for this change in collagen fiber dynamics may include fiber waviness remodeling or cross-linkage by advanced glycation end-products (AGE). The abruptness of collagen fiber engagement is also the model parameter that is most responsible for the decreased compliance at progressed ages.