Solution of Dynamic Problems of Structural Elements Using Simple Polynomial Approximations

1991 ◽  
Author(s):  
Patricio A. A. Laura
Keyword(s):  
Orthogonal Polynomials ◽  
Optimization Procedure ◽  
Structural Elements ◽  
Dynamic Problems ◽  
Structural Element ◽  
Base Function ◽  
Polynomial Approximations ◽  
Deformable Bodies ◽  
Rational Procedure ◽  
Coordinate Functions

Abstract A survey of studies dealing with vibrating structural elements using simple polynomial approximations in connection with Rayleigh-Ritz or Galerkin-type methods is presented. The classical use of polynomials when solving dynamic problems of deformable bodies consists of constructing a set of coordinate functions in such a way that they satisfy at least the essential boundary conditions and that they represent “reasonably well” the deformation field of the structural element under study. An alternative and more rational procedure has been developed and used in recent years whereby orthogonal polynomials are used. A “base function” is constructed and then one generates a set of orthogonal polynomials using the Gram-Schmidt or equivalent procedure. The present paper presents comparisons of numerical results in the case of different types of vibrating structural elements Special emphasis is placed on Rayleigh’s optimization procedure which consists of taking one of the exponents of the polynomial coordinate functions as an optimization parameter “γ”. Since the calculated eigenvalues constitute upper bounds, by minimizing them with respect to “γ” one is able to optimize the eigenvalues.

Multi-Criteria Optimization of a Two-Spar Composite Wing for a Light Aircraft

2021 ◽  
pp. 76-87
Author(s):  
O.V. Tatarnikov ◽  
W.A. Phyo ◽  
Lin Aung Naing
Keyword(s):  
Finite Element Analysis ◽  
Software Package ◽  
Optimization Procedure ◽  
Structural Elements ◽  
Structural Element ◽  
Element Analysis ◽  
Optimization Criteria ◽  
Optimization Parameters ◽  
Nonlinear Static ◽  
Composite Wing

The article considers the results of optimization of the two-spar composite wing for the K-8 training aircraft. The geometric characteristics of the main structural elements of the wing such as spars, ribs and skin; orientation angles of the reinforcing layers and their thicknesses for each wing structural element, as well as the type of composite material and cost were selected as optimization parameters. The proposed optimization procedure includes several steps; each step uses a multi-criteria approach. The minimum deflection, weight, and cost are taken as optimization criteria. All the necessary calculations for selecting the optimal optimization parameters were performed using nonlinear static finite element analysis in the FEMAP software package.

STRUCTURAL RELIABILITY ANALYSIS BASED ON P-BOXES

2020 ◽  
Vol 92 (6) ◽  
pp. 51-58
Author(s):  
S.A. SOLOVYEV ◽  
Keyword(s):  
Probability Distribution ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Random Variable ◽  
Strength Criterion ◽  
Structural Elements ◽  
Structural Element ◽  
Limit States ◽  
Distribution Shape

The article describes a method for reliability (probability of non-failure) analysis of structural elements based on p-boxes. An algorithm for constructing two p-blocks is shown. First p-box is used in the absence of information about the probability distribution shape of a random variable. Second p-box is used for a certain probability distribution function but with inaccurate (interval) function parameters. The algorithm for reliability analysis is presented on a numerical example of the reliability analysis for a flexural wooden beam by wood strength criterion. The result of the reliability analysis is an interval of the non-failure probability boundaries. Recommendations are given for narrowing the reliability boundaries which can reduce epistemic uncertainty. On the basis of the proposed approach, particular methods for reliability analysis for any structural elements can be developed. Design equations are given for a comprehensive assessment of the structural element reliability as a system taking into account all the criteria of limit states.

scholarly journals Structural vehicle impact loading

2013 ◽  
Vol 11 (3) ◽  
pp. 285-292
Author(s):  
Dragoslav Stojic ◽  
Stefan Conic
Keyword(s):  
Impact Analysis ◽  
Impact Loads ◽  
Structural Elements ◽  
Structural Element ◽  
Static Loads ◽  
Equivalent Static Loads ◽  
Vehicle Impact ◽  
Dynamic Forces ◽  
Force Intensity

In contemporary design, vehicle impact into the structures is paid great attention since they can be dominant, depending on the type of structure. The key issue in the vehicle impact analysis is the proper determination of intensity and way of action of dynamic forces on the structural element and its behavior after the imparted load. The Eurocodes, in the annexes provide recommendations for determination of force intensity depending on mass and velocity of the colliding vehicle. Equivalent static loads causing approximate effects on the structural elements are used as quite approximate and efficient methods. The paper comprises the analysis of deformation of columns having the same characteristics, exposed to impact loads via the equivalent static loads, depending on the stress state in columns, and a comparative analysis has been done.

scholarly journals Fish densities associated with structural elements of oil and gas platforms in southern California

2019 ◽  
Vol 95 (4) ◽  
pp. 639-656 ◽  
Author(s):  
Erin L Meyer-Gutbrod ◽  
Li Kui ◽  
Mary M Nishimoto ◽  
Milton S Love ◽  
Donna M Schroeder ◽  
...  
Keyword(s):  
Habitat Use ◽  
Southern California ◽  
Oil And Gas ◽  
Fish Assemblages ◽  
Fish Habitat ◽  
Artificial Reef ◽  
Offshore Structures ◽  
Structural Elements ◽  
Structural Element ◽  
Young Of The Year

There are thousands of offshore oil and gas platforms worldwide that will eventually become obsolete, and one popular decommissioning alternative is the "rigs to reefs" conversion that designates all or a portion of the underwater infrastructure as an artificial reef, thereby reducing the burden of infrastructure removal. The unique architecture of each platform may influence the size and structure of the associated fish assemblage if different structural elements form distinct habitats for fishes. Using scuba survey data from 11 southern California platforms from 1995 to 2000, we examined fish assemblages associated with structural elements of the structure, including the major horizontal crossbeams outside of the jacket, vertical jacket legs, and horizontal crossbeams that span the jacket interior. Patterns of habitat association were examined among three depth zones: shallow (<16.8 m), midwater (16.8–26 m), and deep (>26 m); and between two life stages: young- of-the-year and non-young-of-the-year. Fish densities tended to be greatest along horizontal beams spanning the jacket interior, relative to either horizontal or vertical beams along the jacket exterior, indicating that the position of the habitat within the overall structure is an important characteristic affecting fish habitat use. Fish densities were also higher in transects centered directly over a vertical or horizontal beam relative to transects that did not contain a structural element. These results contribute to the understanding of fish habitat use on existing artificial reefs, and can inform platform decommissioning decisions as well as the design of new offshore structures intended to increase fish production.

Crystal structure of coalingite

1971 ◽  
Vol 38 (295) ◽  
pp. 286-294 ◽  
Author(s):  
J. Pastor-Rodriguez ◽  
H. F. W. Taylor
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Water Molecules ◽  
Structural Elements ◽  
Structural Element ◽  
X Ray ◽  
Octahedral Sites ◽  
Carbonate Ions ◽  
Disordered Layer ◽  
Ray Methods

SummaryThe crystal structure of coalingite (Mg10Fe2(OH)24(CO3)·2H2O) has been determined using single-crystal X-ray methods. The mineral is trigonal, with space group Rm, aH = 3·12, cH = 37·4 Å, Z = ½, and (0001) cleavage. The structure is of a layer type, and is based on a structural element about 12·5 Å thick in the c-direction and consisting of two brucite-like layers and one disordered layer containing carbonate ions and water molecules and resembling those in sjögrenite and pyroaurite. The unit cell comprises three of these structural elements stacked together in the c-direction. The Mg2+ and Fe3+ ions are randomly distributed among all the octahedral sites of the brucite-like layers. The structure closely resembles those of sjögrenite and pyroaurite, but has two brucite-like layers between each CO32−−H2O layer where these have one. There is a tendency to random interstratification, and the crystals appear to contain intergrown regions of brucite and of sjögrenite or pyroaurite. Coalingite-K probably has a similar structure, but with three brucite-like layers between each -H2O layer; its idealized formula is probably Mg16Fe2(OH)36(CO3).2H2O.

Control of Vibration Flow at the Joint of an L-Shaped Frame

2007 ◽  
Author(s):  
C. Mei
Keyword(s):  
Vibration Control ◽  
Control Strategy ◽  
Mechanical Systems ◽  
Structural Elements ◽  
Structural Components ◽  
Structural Element ◽  
Shaped Beam ◽  
Structural Joint ◽  
Structural Joints ◽  
Vibration Problems

There has been an increasing interest in vibration control in recent years. This is due to demands for mechanical structures to be lighter and faster. Lighter and faster structures are more prone to vibrations. Hence, there is an imperative need for practical solutions to vibration problems in complex practical mechanical systems. Regardless of the complexity of a structure, from wave vibration standpoint, it consists of only two basic types of structural components, namely, structural elements and structural joints. In this paper, a control strategy is developed for controlling vibrations flowing from one structural element to another through the structural joint. An L-shaped beam is studied as an example structure. Numerical results are given.

Finite Elements in Time and Space

1969 ◽  
Vol 73 (708) ◽  
pp. 1041-1044 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf
Keyword(s):  
Finite Elements ◽  
Linear Equations ◽  
Time Integration ◽  
Fixed Time ◽  
Time Interval ◽  
Structural Elements ◽  
Dynamic Problems ◽  
System Of Linear Equations ◽  
Interpolation Procedure ◽  
Variational Statement

The present paper seeks to apply the ideas of discretisation to time dependent phenomena. As a suitable variational statement we may use Hamilton's principle. In practise this means that the time is discretised into a set of finite elements which are taken to be the same for all structural elements. A finite element in time consists simply of a fixed time interval. In our present discussion we detail in particular the case when at the beginning and end of the time interval the generalised displacements and velocities are given. For dynamic problems this is the minimum of information required, but the technique may easily be extended to account for additional “timewise degrees of freedoms”. Introducing an appropriate interpolation procedure we may obtain the displacement and velocity at any instant of time. It is then possible to carry out in the variational statement the time integration explicitly and to obtain hence a system of linear equations. The method is extremely simple, since the time interpolation of all structural freedoms of an element in space is the same. We also demonstrate that the general case of a multi-degree of freedoms system can be made to depend on the matrices which describe the unidimensional motion of a mass point.

scholarly journals Damaged Flexibility Matrix Method for Damage Detection of Frame Buildings

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Luis S. Vaca Oyola ◽  
Mónica R. Jaime Fonseca ◽  
Ramsés Rodríguez Rocha
Keyword(s):  
Damage Detection ◽  
Matrix Method ◽  
Structural Damage ◽  
Numerical Models ◽  
Structural Elements ◽  
Structural Element ◽  
New Approach ◽  
Building Model ◽  
Flexibility Matrix ◽  
Frame Buildings

This study presents the damaged flexibility matrix method (DFM) to identify and determine the magnitude of damage in structural elements of plane frame buildings. Damage is expressed as the increment in flexibility along the damaged structural element. This method uses a new approach to assemble the flexibility matrix of the structure through an iterative process, and it adjusts the eigenvalues of the damaged flexibility matrices of each system element. The DFM was calibrated using numerical models of plane frames of buildings studied by other authors. The advantage of the DFM, with respect to other flexibility-based methods, is that DFM minimizes the adverse effect of modal truncation. The DFM demonstrated excellent accuracy with complete modal information, even when it was applied to a more realistic scenario, considering frequencies and modal shapes measured from the recorded accelerations of buildings stories. The DFM also presents a new approach to simulate the effects of noise by perturbing matrices of flexibilities. This approach can be useful for research on realistic damage detection. The combined effects of incomplete modal information and noise were studied in a ten-story four-bay building model taken from the literature. The ability of the DFM to assess structural damage was corroborated. Application of the proposed method to a ten-story four-bay building model demonstrates its efficiency to identify the flexibility increment in damaged structural elements.

Structural Steel Performance Following Severe Earthquake Loading

2011 ◽  
Vol 25 (31) ◽  
pp. 4149-4153
Author(s):  
W. G. Fergusona ◽  
C. K. Seal ◽  
M. A. Hodgson ◽  
G. C. Clifton
Keyword(s):  
Plastic Strain ◽  
Structural Steel ◽  
Central Business District ◽  
Steel Structures ◽  
Earthquake Loading ◽  
Structural Elements ◽  
Steel Buildings ◽  
Structural Element ◽  
Tension And Compression ◽  
Business District

The second Christchurch earthquake on February 22, 2011, Magnitude 6.35, generated more intense shaking in the Central Business District than the September 4, 2010 Darfield earthquake, Magnitude 7.1. The second earthquake was closer to the CBD and at shallow depth, resulting in peak ground accelerations 3 times higher. There was significant failure of unreinforced masonry buildings and collapse of a few reinforced concrete buildings, leading to loss of life. Steel structures on the whole performed well during the earthquake and the plastic, inelastic deformation was less than expected given the strength of the recorded ground accelerations. For steel buildings designed to withstand earthquake loading, a design philosophy is to have some structural elements deform plastically, absorbing energy in the process. Typically elements of beams are designed to plastically deform while the columns remain elastic. In the earthquake some of these elements deformed plastically and the buildings were structurally undamaged. The question which then arises is; the building may be safe, but will it withstand a further severe earthquake? In other words how much further plastic work damage can be absorbed without failure of the structural element? Previous research at Auckland on modern structural steel, where the steel was prestrained various levels, to represent earthquake loading, the toughness was determined, as a function of prestrain for the naturally strain-aged steel. Further research, on the same steel, investigated life to failure for cyclic plastic straining in tension and compression loading at various plastic strain amplitudes. This work has shown that provided the plastic strain in the structural element is in the range 2 – 5% the steel will still meet the relevant NZ Standards. To determine the remaining life the plastic strain must be determ ined then the decision made; to use the building as is, replace the structural element or demolish.

Design Curves for High-Cycle Fatigue Loaded Structural Elements

2013 ◽  
Vol 752 ◽  
pp. 135-144 ◽  
Author(s):  
Zsuzsanna Koncsik ◽  
János Lukács
Keyword(s):  
High Cycle Fatigue ◽  
Empirical Method ◽  
Fatigue Tests ◽  
Structural Elements ◽  
Cycle Fatigue ◽  
Structural Element ◽  
Fatigue Design ◽  
Structural Details ◽  
Important Design

Frequently, the cause of the failure of different structures or structural elements is the cyclic loading. Both fatigue design curves and methods for determination of these curves can be found in the literature. Even so, there are structural details whereabouts executing of examinations is necessary. The aims of the study are as follows: to give a short summary of important design curves can be found in different standards or specifications; and to demonstrate of own high cycle fatigue tests on a soldered structural element and the comparing of our results and the results of an empirical method.

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