Irregular Distribution Of Mass Research Articles

Multipole Representation of the Gravitational Field for Asteroid (16) Psyche

An approach to calculating multipole approximations of the gravitational potential of small celestial bodies with an irregular mass distribution is demonstrated for the asteroid (16) Psyche as an example.

Analytical Modelling of T-Shaped Monolithic & Independent RCC Buildings

Abstract: During an earthquake the behaviour of the building depends on its overall shape, size & geometry. Now a day’s many buildings are asymmetric in plan and elevation because everyone wants to win the race of aesthetically beautiful and complex structures. Due to irregular distribution of mass, stiffness and strength, it may cause serious damage in structural system. There are various types of irregularities in the buildings depending upon their location and scope. Mainly two types of irregularities as per IS – 1893 (Part-1)-2002. are a) plan or horizontal irregularities b) vertical irregularities. Irregularity in structure makes analysis of the seismic behaviour very complicated. The objective of present study is to analyze and compare the behaviour of T shape monolithic and independent RCC structure under seismic loading. The comparison of both structures is studied by calculating, finding and tabulating comparative values of displacement, base moments and shear values. The study reflects that with change in structure i.e. the behaviour of structure towards earthquake changes, nodal displacement, moment, and base shear values shows drastic changes towards resistivity against seismic forces. The soft computing tool and commercial software STAAD-Pro is used for modelling and analysis also the study done over here thus helps to understand effect of earthquake on both structures for achieving stable and safe structure

Torsional Improvements in a Multistoried Building with Plan Irregularities

Irregular buildings consist of large number of modern urban structures. Though some buildings look symmetrical in plan might have irregular distribution of mass, strength and stiffness along the plan and height of the buildings. In common sense, a building with a regular geometry is supposed to be regular building. While the building is designed to be used for different functions along the building area and along the building plan the presence of opening, staircase positioning and positioning of the shear/core wall for different purpose like lift and HVAC (Heating, Ventilation and Air Conditioning) leads to the irregularity in the plan. Ultimately, torsion irregularity occurs, which if remains not taken care properly may create substantial damage of the building structures. The purpose of this study is to determine the conditions for excessive torsional irregularity and solve them with the proper positioning of the shear wall to counter the torsional behavior of the building. A linear response analysis was conducted and the studied structures were both six- storey buildings. First building has opening left for different purpose like lift and HVAC systems. While the second building has shear wall for lift at the edge of the building. Though both buildings seem fine with their geometrical orientation after the analysis torsional irregularity was evident. The proper placement of the shear wall has been used to stiffen the building to counter for the torsional modal and make to regular in terms of the mass and stiffness distribution.

Seismic Analysis of Unsymmetrical Buildings Compering with Regular Building

Structural analysis of building is taken into account for finding out the behaviors of a structure when subjected to some external force acting on building. Building structural design for seismic loads is critical for structural safety during large ground movementsBuildings with symmetrical and unsymmetrical plan geometry, strength, and stiffness are also varied. During earthquakes, structures with a symmetric distribution of stiffness and strength in plan experience combined lateral and torsional motions.Previous earthquakes, in which many reinforced concrete structures were badly damaged or collapsed, highlighted the need to assess building seismic performance. Earthquakes can cause irregular distribution of mass, stiffness and strengths i.e., unsymmetrical buildings may cause heavy damage in structural members. Buy referring this paper it is concluded that symmetric buildings perform better than un-symmetric buildings when subjected to earthquake forces.

The fractal version of the bond‐based peridynamics method

AbstractThis article presents a new formulation of bond‐based peridynamic theory (PD) encompassing material texture heterogeneity through fractal geometry concepts and transforming all relevant variables from Euclidean space to fractal space. The heterogeneity incorporation is realized through the introduction of a linear transformation fractal coefficient (LTFC). By considering a mean value for all LTFCs of all spatial coordinates. For example, x, y, z, and using the relationship between fractal dimension and the Hurst exponent . We present a fractal version of the bond‐based PD method that the equation of motion is conformed to fractal space. Validation of the formulation is accomplished in two steps: first, the effect of irregular mass distribution is characterized by the fractal dimension of the fracture surface roughness through experimental results of a series of single‐edge notched tensile tests of a ductile material. In the next step, the proposed formulation is calibrated with the fractal dimension obtained experimentally. The results are compared with the classical bond‐based PD formulation and the finite element analysis results. The obtained results in this article indicate that the irregular mass distribution of material can be introduced into particle‐based numerical methods using an adequate fractal exponent. The fractal version provides a good approximation of the fracture behavior of materials.

Seismic behaviour of irregular steel frames with beam and joint energy dissipation

This paper investigates the seismic performance of steel moment resisting frames, exploring the potential for energy dissipation not only in the beams but in the beam-to-column joints too. Such an approach practically doubles the possible locations for dissipative zones in the structure but on the other hand places requirements for ductile behaviour on the connections. A design methodology that facilitates the formation of plastic hinges in the beam-to-column joints and the beams at the same time, is presented and examined in comparison to typically designed frames with rigid joints. A number of 24, 2D regular and irregular frame configurations are studied numerically, employing both nonlinear static and dynamic analyses. The examined configurations involve either irregular mass distribution across the floors or stiffness discontinuities of the framing across the floors and the bays. The results indicate a great reduction in ductility demands for the frames with energy dissipation in the beams and the joints concurrently, while other metrics of their seismic response, such as interstorey drifts and lateral capacity remain practically unaffected.

Intact archeological human bones and age at death studied with transmission x‐ray diffraction and small angle x‐ray scattering

High-energy, wide-angle x-ray scattering (WAXS, x-ray diffraction) and small-angle x-ray scattering (SAXS) were used to study intact human second metacarpal bones (mc2) from two UK archeological sites. A novel method correcting for irregular mass distribution was applied in these transmission geometry experiments done at beamline 1-ID of the Advanced Photon Source. The authors asked whether there were age-at-death-related changes in carbonated apatite (cAp) lattice parameters and whether SAXS could detect collagen D-period peaks in the archeological mc2. For each of the two sites, Ancaster and Wharram Percy in England, six female mc2s were studied; for each site, two were from each of three age-at-death cohorts (young, 18–29 years; middle, 30–49 years; old ≥50 years) along with a modern control mc2. The Rietveld method was applied to the WAXS patterns to provide precise lattice parameter values. The cAp lattice parameters did not correlate with age-at-death estimated from dental wear. From WAXS and the 00.2 diffraction peak widths, four archeological mc2s possessed coherently scattering domain lengths (crystallite c-axis sizes) that matched that of the modern mc2; SAXS revealed the same four archeological mc2 had D-period peak intensities equivalent to that of the modern mc2. The other eight archeological mc2s had significantly larger crystallite sizes (than the modern mc2) and weak or absent D-period peaks, differences attributed to diagenetic changes. Based on these data, the authors suggest that WAXS 00.2 peak width and SAXS D-period peak intensity can be used with intact bones to select those likely to retain largely unaltered tissue nanostructure, which might be required for other analyses. Taken as a whole, the results suggest detecting age-related deterioration in nanostructural features may be difficult in bone showing significant bioerosion.

A simplified procedure for the seismic analysis of RC moment resisting setback frames

Irregularity in elevation of buildings is increasingly popular in modern urban construction. One of the prominent forms of vertically irregular frames is the setback building frames. The seismic performance of buildings with irregular distribution of mass, stiffness, and strength along the height may be significantly different from that of regular buildings. The present paper focuses on quantification of irregularity and studying the effect of irregularity on the seismic performance of setback building frames. An index namely Geometric Regularity Index (GRI), calculated based on the geometric parameter of the building frame, is proposed in the study to quantify the vertical irregularity of setback building frames. 55 numbers of 3 bay frames with stories 5, 7, 9, 11 and 13, with varying levels of irregularity, are considered in the study. Linear dynamic analysis of the frames is performed in ETABS using response spectrum method. The proposed index is correlated with the actual seismic response of the structure such as base shear and overturning moment. Based on the results of analysis, a simple method which employs the GRI of the frame is proposed to estimate the seismic responses such as base shear and overturning moment at the base. The proposed method is found to estimate the seismic response of setback frames with reasonable accuracy.

Seismic behaviour of stiffness irregular steel frames under mainshock–aftershock

Generally, the buildings located in earthquake-prone regions are subjected to a sequence of earthquakes. The sequence of earthquakes is termed as mainshock–aftershock (MS–AS). Most of the time the rehabilitation of structure before the occurrence of aftershock cannot be carried out due to a short interval of time between mainshock and aftershock results in additional damage to the structure. The irregular distribution of mass, stiffness and strength along the height of the building may exhibit the poor seismic performance of the structures. The present study examined the influence of stiffness irregularity on seismic demands of 3-, 6- and 9-storey steel moment-resisting frames by comparing the mean seismic demands on reference regular frames under mainshocks and MS–AS seismic sequences. Stiffness irregular frames are obtained by modifying the stiffness at three different locations (bottom, middle and top storey) along with the height of reference regular frame. MS–AS seismic sequences are generated by using a randomized approach. The comparison between reference and stiffness irregular frames shows that the effect of stiffness irregularity on the height-wise variation of interstorey drift ratio is significant. Results of the effect of MS–AS seismic sequence show that aftershock increases the structural responses of both reference regular and stiffness irregular frames.

Reliability-Based Seismic Assessment of Multi-Story Box System Buildings under the Accidental Torsion

ABSTRACT Performance analysis of reinforced concrete (RC) buildings during past earthquakes has shown that irregular distribution of mass, stiffness, and strength may cause severe damage in structural elements. Accidental torsion, one of the most common reasons of damage and failure under the strong ground motions, is a complex phenomenon in which several variables are involved. The box-type structural system is considerably sensitive to torsion due to shear wall arrangement and that the torsional mode which governs structural response. Thus, understanding and evaluating accidental torsion is a fundamental step in seismic reliability evaluation of this structural system in comparison with other common structures. Therefore, in this study, seismic sensitivity of the box-type structural system is evaluated for various configurations of mass, stiffness, and strength centers. Several analyses, such as eigen-value, push-over, nonlinear time history, and seismic reliability analysis are performed using artificial records to predict structural characteristics and probabilities of failure. The results show that the mass eccentricity has a greater effect on the seismic response in comparison with the strength and stiffness eccentricities. The most critical condition occurs when the mass and stiffness centers are shifted in the same direction, so the story drift under the design and maximum credible earthquakes are 2.45 and 2.26 times the symmetrical model drift, respectively. Furthermore, it is shown that this box-type structural system demonstrates acceptable seismic reliability under the accidental torsion since the main elements of lateral bearing system remain in an immediate occupancy performance level under the design earthquake.

Equilibrium points stability analysis for the asteroid 21 Lutetia

This work investigates the stability of the equilibrium points that occur around the asteroid (21) Lutetia, assuming that this body has a constant velocity of rotation and is immersed in a gravitational field, whose force of attraction presents a perturbation with respect to the central force due to the irregular mass distribution of the asteroid. For the calculation of the potential, as well as of the effective potential, was used the method of the expansion of the potential in series, associated to the asteroid decomposition in tetrahedral elements. The zero velocity curves for a massless particle orbiting the gravitational environment were analyzed. The linearized dynamic equation in the vicinity of the equilibrium points, the associated characteristic equation, and the Jacobi constant were calculated. The validation of the results was ratified by simulations of trajectories around these equilibrium points, considering the gravitational field modelled. It should be emphasized the general nature of the procedures adopted in this work, that is, they can be applied to any other asteroid.

Large-scale modeling of parametric asteroid surfaces using polynomial series

In the last twenty years, numerous deep space probes have been sent to space to detect asteroids, comets and planetary satellites, indicating that small Solar System bodies have become one of the main targets for deep space exploration. Many of asteroids are remnants of the materials from which the solar system accreted. The asteroid contains information about the origins and development of the solar system. The size and shape of the asteroid contains their thermal, collision, and kinetic history, and is fundamental to the analysis of gravitational field and dynamics of the asteroid. Studies on the asteroid geological structure shows that most asteroids have asymmetric and irregular mass distributions. It posed a challenge in accurately modelling of such asteroids’ surfaces. And for the solar system small bodies, the most widely-applied method is to discretize their surfaces is the polyhedron method. However, the shape model of the asteroid obtained by polyhedron method is triangular mesh model. In order to study the dynamics of the asteroid’s surface, we need to build a continuous, analytical model of asteroid surfaces. For these questions, the following research is done in this paper. Firstly, the CALD algorithm which controls both length distortion and area distortion is used to map the sample point data of the asteroid to the unit sphere. After obtaining the bijection relationship between the asteroid surface and the unit sphere, the polynomial series is used as the basis function to characterize the bijection relationship. Then, the sample point coordinates and the corresponding coordinates on the unit sphere are substituted into the polynomial model established to obtain a set of large-scale linear equations. Since the fundamental function of polynomial series is non-orthogonal, the system is a pathological equation. In this paper, the method of solving large-scale ill equations is adopted to control the error of solving equations within acceptable range. Finally, after the establishment of the polynomial model, this paper discusses in detail the modified parameters in the polynomial model that affect the model accuracy.

Numerical Evaluation of Seismic Response of Asymmetrical Reinforced Concrete Frame Buildings

Asymmetrical multi-storey buildings are almost unavoidable in modern structures due to various types of useful and architectural requirements. Latest earthquakes showed that irregular distribution of mass, stiffness and strength cause serious damage in building structural systems. This paper investigates the numerical simulation of buildings with plan irregularity and presents a case study to demonstrate the numerical evaluation of the seismic response of a three real plan-asymmetric reinforced concrete building tested at full scale at the European Laboratory for Structural Assessment of the Joint Research Center, Ispra / Italy within the SPEAR project. The structural evaluation performed through a validated Finite Elements Package, modeled by the general purpose ABAQUS, which is able to run accurate analysis, in particular nonlinear static and dynamic analysis considering both geometric nonlinearity and material inelasticity.Adequacy of the numerical modeling is verified by comparing numerical and experimental results through evaluation of the seismic capacity and dynamic characteristics of the building. The provisions of the adopted seismic code for designing such buildings are also checked over and done with the nonlinear static and dynamic analysis by verifying the proficiency of an analytical model for simulating the nonlinear response of structures considered to conduct an investigation into experiments.

Vertical Irregularity of Buildings: Regularity Index versus Seismic Risk

AbstractThe seismic performance of buildings with irregular distribution of mass, stiffness, and strength along the height may be significantly different from that of regular buildings. Design code...

Dynamics of a compound celestial body and a massive point, subjected mutual attraction

A problem of motion of a massive particle in a field of attraction of a homogeneous dumb-bell body consisting of a pair of balls is considered. The balls are assumed intersecting each other. Their radii can be unequal. An approximate expression for the potential of attraction is deduced. Within an assumption on uniform rotation of the dumb-bell about its central axis of inertia differing from the axis of symmetry positions of relative equilibria of the massive particle (libration points) are investigated.As is known, there exist celestial bodies, seeming composed by large lobes, somehow connected or penetrating one into another. Evident irregularity in their mass distribution implies difficulties in description of gravitational fields using classical approach, based on utilization of spherical harmonics (cf.[1]). Extending another approach, based on utilization of single dumb-bells [2,3] or triangles with masses, concentrated in vertexes [4–7], we discuss a possibility of exploitation of real and complexified dumb-bells for description of Newtonian attraction. For some examples, existence, stability and bifurcations of uniformly rotating stationary configurations of such bodies and massive points under mutual attraction were studied without assumptions on a mass ratio of the gravitating bodies. This means, that the results cover not only the case, when the body is much more massive than the point, but also the case when two masses are comparable, as well as the case, when the point is considerably more massive than the body. In the latter case the body with irregular mass distribution orbites about a massive immobile primary.

On relative equilibria of mutually gravitating massive point and triangular rigid body

AbstractPlanar motions of a triangular body and a massive point under the action of mutual Newtonian attraction are studied. For the first formulation the triangle is assumed to be composed of three massive points. For the second formulation it is constructed with three homogeneous rods. Some partial solutions are observed within the analysis of the geometry of mass distribution.The investigation is motivated by the problem of motion of spacecrafts near asteroid-like celestial objects possessing irregular mass distribution. Comparison of dynamical effects for two types of mass distribution is another goal of the research.Problems appearing because of irregularities in mass distributions have been known for a long time. Certain approaches to the description of motions under attraction as well as qualitative particulars of dynamics are discussed by Demin (1963), Burov & Karapetyan (1995), Buchin & Burov & Troger (2008), Burov & Guerman & Sulikashvili (2010), Kholshevnikov & Kuznetsov (2011), Beletsky & Rodnikov (2011) and Scheeres (2012).

2A11 In-plane vibration of micro ring with irregular mass distributions(The 12th International Conference on Motion and Vibration Control)

Vibration characteristics are an important factor for the stability of structures. Up to now, a ring model is used as a typical model for structures, and then irregularity of point mass distribution has been a main issue for the research works. In this paper, in-plane vibration of thermo-elastic micro ring structures with finite sized imperfection is to investigate. Then, in-extensionality of the model is assumed, and multiple local deviations in structure are to be represented by Heaviside step functions. Fourier's one-dimensional heat conduction equation is to analyze, and Laplace transform method is used to solve the governing equations to obtain analytical solution. In order to determine Quality factor (Q-factor) of ring model, primarily, the split of the natural frequencies are discussed with the irregularity of mass and stiffness. And the mode shapes are compared between perfect and imperfect ring models.

Modal identification of structures by a novel approach based on FDD-wavelet method

An important application of system identification in structural dynamics is the determination of natural frequencies, mode shapes and damping ratios during operation which can then be used for calibrating numerical models. In this paper, the combination of two advanced methods of Operational Modal Analysis (OMA) called Frequency Domain Decomposition (FDD) and Continuous Wavelet Transform (CWT) based on novel cyclic averaging of correlation functions (CACF) technique are used for identification of dynamic properties. By using this technique, the autocorrelation of averaged correlation functions is used instead of original signals. Integration of FDD and CWT methods is used to overcome their deficiency and take advantage of the unique capabilities of these methods. The FDD method is able to accurately estimate the natural frequencies and mode shapes of structures in the frequency domain. On the other hand, the CWT method is in the time-frequency domain for decomposition of a signal at different frequencies and determines the damping coefficients. In this paper, a new formulation applied to the wavelet transform of the averaged correlation function of an ambient response is proposed. This application causes to accurate estimation of damping ratios from weak (noise) or strong (earthquake) vibrations and long or short duration record. For this purpose, the modified Morlet wavelet having two free parameters is used. The optimum values of these two parameters are obtained by employing a technique which minimizes the entropy of the wavelet coefficients matrix. The capabilities of the novel FDD-Wavelet method in the system identification of various dynamic systems with regular or irregular distribution of mass and stiffness are illustrated. This combined approach is superior to classic methods and yields results that agree well with the exact solutions of the numerical models.

Validation and improvement of N1 method for pushover analysis

Many of the non-linear static methods for seismic assessment of buildings according to modern structural codes are based on the well-known N2 procedure. A more intuitive pushover procedure, N1, has recently been proposed. Its main advantage is that the explicit evaluation of an equivalent SDOF system is not required. The N1 method has been proved to provide the same accuracy as N2, but only when a lateral load distribution proportional to the first mode shape is involved. After a brief description of the main differences between the two methods, an improved version, the N1 corrected method, is presented here. It is more consistent with N2, also when constant acceleration lateral load patterns are applied. The N1 corrected method is validated according to an extensive parametric investigation of a set of case studies on steel and R/C frames, with regular and irregular mass distribution in height.

Probabilistic seismic performance evaluation of non-geometric vertically irregular steel buildings

The seismic performance of structures with irregular distribution of mass, stiffness and strength along the height, may be significantly different compared to regular structures, depending on the limit-state or the level of seismic intensity considered. In the framework of probabilistic performance based earthquake engineering, it is possible to quantify the effects of vertical irregularities on the seismic performance of structures. In this study, the seismic performance of different non-geometric vertical irregular structures is compared to a regular structure at various performance levels with a probabilistic approach. The results show that the non-uniform distribution of lateral resisting properties over the height of structure influences the seismic performance, especially at the limit-states close to collapse until global dynamic instability. These effects may be on the seismic intensity capacity and/or on the ductility capacity of the structure, based on the type and the position of vertical irregularities. Also from the standpoint of a probabilistic seismic performance based design, the vertical irregularities increase the mean annual frequency of exceeding the GI performance level by about 5% to 30%.