scholarly journals Progressive limit state at critical levels of internal potential energy of deformation

Vestnik MGSU ◽  
2021 ◽  
pp. 1324-1336
Author(s):  
Leonid Yu. Stupishin
Keyword(s):  
Potential Energy ◽  
Infinite Number ◽  
Extreme Values ◽  
Limit State ◽  
The Self ◽  
Upper And Lower Bounds ◽  
Critical Levels ◽  
Internal Forces ◽  
Stress States ◽  
Internal Potential

Introduction. The work is devoted to one of the main issues of structural mechanics - the determination of the elements in which the limiting state occurs first. At first glance, the task has an infinite number of results, meaning an infinite number of options for loading the system. The problem becomes solvable if one examines the structure of a building (structure) for possible variations in displacements (forces) in the nodes of the structure. For this approach, it becomes possible to determine the main values and vectors of displacement of the system, which correspond to the maximum (minimum) values of deformations (forces) in the rods of the system. As close approaches to the formulation of the problem, one should indicate the theory of the limiting equilibrium of structures under the assumption of the work of the material under flow conditions, where the equality of the work of external forces and internal forces is considered (kinematic method), or possible static stress states of the system for maximum limiting loads (static method). The theory of protecting buildings and structures from progressive collapse seeks to solve similar problems, focusing on options for design solutions that prevent destruction from non-design loads. Materials and methods. To determine the options for the distribution of extreme values of internal forces (deformations) in the system, the problem is formulated in the form of an eigenvalue problem. The latter turns out to be the most convenient mathematical model of the problem, since, in addition to extreme values (as in the optimization problem), it allows one to take into account the values of the problem on the upper and lower bounds. The theoretical basis for the formulation of the problem is the criterion of the critical levels of the internal potential energy of the system, which makes it possible to find the self-stress states of the structure corresponding to the limiting states of the structural elements. Results. The methodology for solving the problem is illustrated by the example of a statically indeterminate five-rod truss, which was also considered by other authors. The matrix formulation of the problem and a detailed algorithm for its solution are given. It is shown that the values of the internal forces in the rods, obtained using the traditional method, are in the interval between the maximum and minimum main values of the self-stress state of the system. Solutions are given at each of the critical energy levels corresponding to the disconnection of bonds from work.

scholarly journals Problems of beam bending solution on the basis of variation criterion of critical energy levels

Vestnik MGSU ◽  
2021 ◽  
pp. 306-316
Author(s):  
Leonid Yu. Stupishin ◽  
Mariya L. Moshkevich
Keyword(s):  
Potential Energy ◽  
Physical Nature ◽  
Structural Mechanics ◽  
Critical Levels ◽  
Pure Bending ◽  
Concentrated Force ◽  
Transverse Bending ◽  
Internal Potential ◽  
Bending Of Beams ◽  
Variational Formulations

Introduction. The article is devoted to the development of variational formulations of structural mechanics problems using the example of the problems of bending beams. The existing variational approaches, the nonlinear theory of bending of beams, as well as the classical methods of resistance of materials, are not able to explain a number of issues related to the discrepancy between the results of theory and experiments, for example, in problems of pure and transverse bending of beams. To solve these issues, variational formulations and the criterion of critical levels of the internal potential energy of deformation, developed by the authors, are used. Materials and methods. For the internal potential energy of a deformed body, the stationarity condition at critical levels is written, which makes it possible to obtain equations of state that describe the self-stress of the structure. It is shown that a mathematical model of the state of a structure at critical levels of potential energy of deformation leads to an eigenvalue problem. The quantities characterizing the formulation of problems when formulating in generalized efforts and generalized displacements are discussed. Results. Using the examples of problems of pure bending and direct transverse bending of simple beams by a concentrated force, the formulation of the problem and the method of its solution are shown. The diagrams of deflections and bending moments are given, and the magnitudes of the amplitude values in the middle of the span are given. It is shown that for simple beams in problems of pure bending and transverse bending, the maximum values of the moments are achieved in the middle of the beam span, as in the experiment. Conclusion. The results are discussed and compared with the data obtained in the theory of flexible rods. It is noted that the dangerous section in two approaches having different physical nature is located in the middle of the beam span. The boundaries of discrepancy between the results for displacements, moments of internal forces and stresses are shown. It is noted that the results obtained according to the linear theory of strength of materials lead to a significant margin of safety. The prospects for the development of the theory of critical levels of internal potential energy of deformation, and the possibility of applying the technique to problems of structural mechanics are discussed.

LBE for Generalized Hydrodynamics

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Potential Energy ◽  
Electric Fields ◽  
Chemical Reactions ◽  
Soft Matter ◽  
Fluid Motion ◽  
Life Sciences ◽  
Scientific Discipline ◽  
The Past ◽  
Generalized Hydrodynamics ◽  
Internal Forces

This chapter presents the main techniques to incorporate the effects of external and/or internal forces within the LB formalism. This is a very important task, for it permits us to access a wide body of generalized hydrodynamic applications whereby fluid motion couples to a variety of additional physical aspects, such as gravitational and electric fields, potential energy interactions, chemical reactions and many others. It should be emphasized that while hosting a broader and richer phenomenology than “plain” hydrodynamics, generalized hydrodynamics still fits the hydrodynamic picture of weak departure from suitably generalized local equilibria. This class is all but an academic curiosity; for instance, it is central to the fast-growing science of Soft Matter, a scientific discipline which has received an impressive boost in the past decades, under the drive of micro- and nanotechnological developments and major strides in biology and life sciences at large.

2. Does form follow function?

2014 ◽  
Author(s):  
David Blockley
Keyword(s):  
Potential Energy ◽  
Degrees Of Freedom ◽  
Minimum Potential Energy ◽  
Form Finding ◽  
Internal Forces ◽  
Minimum Potential ◽  
The Way

In c.15 bc, the Roman Vitruvius stated that a good building should satisfy three requirements: durability, utility, and beauty. ‘Does form follow function?’ examines utility and beauty. It explains that structures are naturally lazy because they contain minimum potential energy. Each piece of structure, however small or large, will move, but not freely as the neighbouring pieces will get in the way. When this happens internal forces are created as the pieces bump up against each other. Force pathways are degrees of freedom and the structure has to be strong enough to resist these internal forces along these pathways. Form-finding structures are exciting and innovative examples of the fusion of engineering and architecture.

scholarly journals R3 fluids

2007 ◽  
pp. 13-33 ◽  
Author(s):  
R. Caimmi
Keyword(s):  
Potential Energy ◽  
Equatorial Plane ◽  
The Self ◽  
Energy Tensor ◽  
Ideal Self ◽  
Random Velocity ◽  
Equilibrium Configurations ◽  
Random Motions ◽  
Self Potential

The current paper is aimed at getting more insight on three main points concerning large-scale astrophysical systems, namely: (i) formulation of tensor virial equations from the standpoint of analytical mechanics; (ii) investigation on the role of systematic and random motions with respect to virial equilibrium configurations; (iii) determination of extent to which systematic and random motions are equivalent in flattening or elongating the shape of a mass distribution. The tensor virial equations are formulated regardless of the nature of the system and its constituents, by generalizing and extending a procedure used for the scalar virial equations in presence of discrete subunits (Landau and Lifchitz 1966). In particular, the self potential-energy tensor is shown to be symmetric with respect to the exchange of the indices, (Epot)pq = (Epot)qp. Then the results are extended to continuous mass distributions. The role of systematic and random motions in collisionless, ideal, self-gravitating fluids is analysed in detail including radial and tangential velocity dispersion on the equatorial plane, and the related mean angular velocity, ?, is conceived as a figure rotation. R3 fluids are defined as ideal, self-gravitating fluids in virial equilibrium, with systematic rotation around a principal axis of inertia, taken to be x3. The related virial equations are written in terms of the moment of inertia tensor, Ipq, the self potential-energy tensor, (Epot)pq, and the generalized anisotropy tensor, ?pq (Caimmi and Marmo 2005, Caimmi 2006a). Additional effort is devoted to the investigation of the properties of axisymmetric and triaxial configurations. A unified theory of systematic and random motions is developed for R3 fluids, taking into consideration imaginary rotation (Caimmi 1996b, 2006a), and a number of theorems previously stated for homeoidally striated Jacobi ellipsoids (Caimmi 2006a) are extended to the more general case of R3 fluids. The effect of random motion excess is shown to be equivalent to an additional real or imaginary rotation, respectively, inducing flattening (along the equatorial plane) or elongation (along the rotation axis). Then it is realized that a R3 fluid always admits an adjoint configuration with isotropic random velocity distribution. In addition, further constraints are established on the amount of random velocity anisotropy along the principal axes, for triaxial configurations. A necessary condition is formulated for the occurrence of bifurcation points from axisymmetric to triaxial configurations in virial equilibrium, which is independent of the anisotropy parameters. A particularization of general relations is made to the special case of homeoidally striated Jacobi ellipsoid, and some previously known results (Caimmi 2006a) are reproduced. .

A Model of Force Generation in a Three-Dimensional Toroidal Cluster of Cells

2012 ◽  
Vol 79 (5) ◽  
Author(s):  
Asha Nurse ◽  
L. B. Freund ◽  
Jacquelyn Youssef
Keyword(s):  
Potential Energy ◽  
Gravitational Potential ◽  
Self Assembly ◽  
Three Dimensional ◽  
Dissipative System ◽  
The Self ◽  
Three Dimensions ◽  
Force Generation ◽  
Gravitational Potential Energy ◽  
Kinetics Of

Observation of the self-assembly of clusters of cells in three dimensions has raised questions about the forces that drive changes in the shape of the cell clusters. Cells that self-assemble into a toroidal cluster about the base of a conical pillar have been observed in the laboratory to spontaneously climb the conical pillar. Assuming that cell cluster reorganization is due solely to surface diffusion, a mathematical model based on the thermodynamics of an isothermal dissipative system is presented. The model shows that the cluster can reduce its surface area by climbing the conical pillar, however, this is at the expense of increasing its gravitational potential energy. As a result, the kinetics of the climb are affected by parameters that influence this energy competition, such as the slope of the conical pillar and a parameter of the model κ that represents the influence of the surface energy of the cluster relative to its gravitational potential energy.

scholarly journals ON DESIGN FEATURES OF PROPPED AND UNPROPPED HYPERSTATIC STRUCTURES

2007 ◽  
Vol 13 (2) ◽  
pp. 123-129 ◽  
Author(s):  
Algirdas Kudzys ◽  
Romualdas Kliukas ◽  
Antanas Kudzys
Keyword(s):  
Reinforced Concrete ◽  
Design Methodology ◽  
Extreme Values ◽  
Limit State ◽  
Ultimate Limit State ◽  
Term Survival ◽  
Partial Factor ◽  
Ultimate Limit ◽  
Composite Steel

An effect of structural and technological features on the design methodology of hyperstatic precast reinforced concrete and composite steel‐concrete structures is discussed. Permanent and variable service, snow and wind loads of buildings and their extreme values are analysed. Two loading cases of precast reinforced concrete and composite steel‐concrete continuous and sway frame beams as propped and unpropped members are considered. A redistribution of bending moments for the ultimate limit state of beams is investigated. A limit state verification of hyperstatic beams by the partial factor and probability‐based methods is presented. It is recommended to calculate a long‐term survival probability of beams by the analytical method of transformed conditional probabilities.

scholarly journals Secondary Moments due to Prestressing with Different Bond at the Ultimate Limit State

2018 ◽  
Vol 26 (1) ◽  
pp. 10-18
Author(s):  
Jaroslav Halvoník ◽  
Peter Pažma ◽  
Radoslav Vida
Keyword(s):  
Limit State ◽  
Plastic Hinge ◽  
Ultimate Limit State ◽  
Critical Cross Section ◽  
Structural System ◽  
Secondary Effects ◽  
Limit States ◽  
Internal Forces ◽  
Ultimate Limit ◽  
Kinematic Mechanism

Abstract Secondary effects of prestressing develop in statically indeterminate structures (e.g., continuous beams) due to the restraint of deformations imposed by hyperstatic restraints. These effects may significantly influence internal forces and stresses in prestressed structures. Secondary effects are influenced by the redundancy of a structural system, which raises the question of whether they will remain constant after a change in the structural system, e.g., due to the development of plastic hinge(s) in a critical cross-section(s) or after the development of a kinematic mechanism, or if they will disappear when the structure changes into a sequence of simply supported beams. The paper deals with an investigation of the behavior of continuous post-tensioned beams subjected to an ultimate load with significant secondary effects from prestressing. A total of 6 two-span beams prestressed by tendons with different bonds were tested in a laboratory with a load that changed their structural system into a kinematic mechanism. The internal forces and secondary effects of the prestressing were controlled through measurements of the reactions in all the supports. The results revealed that the secondary effects remained as a permanent part of the action on the experimental beams, even after the development of the kinematic mechanism. The results obtained confirmed that secondary effects should be included in all combinations of actions for verifications of ultimate limit states (ULS).

scholarly journals Hydraulic Erosion Rate of Reinforced Tailings: Laboratory Investigation and Prediction Model

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Xuanyi Chen ◽  
Xiaofei Jing ◽  
Hai Cai ◽  
Yijun Wang ◽  
Luhua Ye
Keyword(s):  
Potential Energy ◽  
Prediction Model ◽  
Laboratory Investigation ◽  
Erosion Rate ◽  
Failure Modes ◽  
The Self ◽  
Tailings Dam ◽  
Test Results ◽  
Tailings Dams ◽  
Overtopping Failure

Tailings dams are high-potential-energy dams built to store various ore tailings, and the overtopping failure caused by hydraulic erosion is one of the most common failure modes. The characteristics of hydraulic erosion of the reinforced tailings were studied by using the self-made erosion apparatus with four kinds of reinforcement spacing 2.5, 1.7, 1.3, and 1.0 cm, respectively. The test results show a positive correlation between the reinforcement spacing and erosion rate of tailings. Based on the sediment scouring theory, the scouring constant in the erosion rate formula is determined to be 0.056 mm/s; a prediction model for the hydraulic erosion rate of reinforced tailings is established by introducing the collapse coefficient into the results of the overflow test of reinforced tailings. This model can provide a reference for the prediction of overtopping-induced erosion failure of the reinforced tailings dam.

scholarly journals Criteria for the Minimum Operation Length of Internal Forces as a Function of the Development of an Optimum Structure of Machinery Structural Components

2016 ◽  
Vol 21 (4) ◽  
pp. 997-1005 ◽  
Author(s):  
M. Fligiel ◽  
R. Patyk
Keyword(s):  
Potential Energy ◽  
Potential Gradient ◽  
Deformation Energy ◽  
Optimum Structure ◽  
Structural Components ◽  
Energy Potential ◽  
Rigid Structure ◽  
Internal Forces ◽  
The Given

Abstract The present study analyzes the operation length of internal forces (DDSW) understood as the length of the flow of internal forces along the shortest possible internal routes. The operation length of internal forces is determined on the basis of stresses and the given volume in the constructional space. The minimum DDSW of the structure satisfies the criterial conditions of the most rigid structure, where the potential energy of deformation and the deformation energy potential is the same in the whole volume and thus the potential gradient is zero.

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