Showing papers in "Meccanica in 1972"
TL;DR: In this paper, a body having ideally elastoplastic constitutive laws with associated flow laws is considered and a finite elements description is assumed, where the flow laws are described by finite elements.
Abstract: Bodies having ideally elastoplastic constitutive laws with associated flow laws are considered. Finite elements description is assumed.
31 citations
TL;DR: In this article, the dynamic problem of rigid plastic structures subjected to impulsive loading is discussed in matrix notation on the basis of finite element discretization of the structure and piecewise linear approximation of the yield surfaces, using some quadratic programming concepts.
Abstract: This paper discusses the dynamic problem of rigid plastic structures subjected to impulsive loading. A couple of “dual” extremum theorems reduces the problem to the optimization of convex quadratic functions subject to linear inequalities and equations: the first theorem takes as variables stress and accelerations, the second accelerations and plastic multiplier rates. The problem is discussed in matrix notation on the basis of finite element discretization of the structure and piecewise linear approximation of the yield surfaces, using some quadratic programming concepts. The procedure is illustrated by a simple numerical example.
21 citations
TL;DR: The theory of potential operators in Hilbert spaces is applied to a rigorous definition of conservative loading in this article, where the authors show that conservative loading can be expressed as a potential operator in a Hilbert space.
Abstract: The theory of potential operators in Hilbert spaces is applied to a rigorous definition of conservative loading.
19 citations
TL;DR: In this article, the asymptotic stability of linear isotropic Kelvin-Voigt solids subjected to external damping and non-conservative surface tractions which are linear functions of displacements and displacement gradients is considered.
Abstract: The asymptotic stability of linear isotropic Kelvin-Voigt solids subjected to external damping and noncon-servative surface tractions which are linear functions of displacements and displacement gradients is considered. The boundary value problem that is adjoint to the original system is derived, and a variational principle from which these two boundary value problems may be generated is stated. The variational principle serves as a basis for an approximate method (similar to the Ritz method) for solving nonconservative stability problems in which the effects of internal and external damping are present. The method is applied to determine the value of the critical load intensity Qcr in a cantilever and a clamped-simply supported beam subjected to a linearly distributed tangential load as well as to internal and external damping forces. Plots of the variation of Qcr with the two damping parameters are given, and it is shown the nature of the boundary conditions can have a significant effect on the manner in which Qcr varies as a function of the damping parameters.
15 citations
TL;DR: In this article, a comprehensive analysis of geometrically non-linear structural problems by the finite element method is presented, based on a variational principle stating the incremental equilibrium through the stationarity of a functional that could be defined as the incremental total potential energy.
Abstract: The paper shows a comprehensive analysis of geometrically non linear structural problems by the finite element method. The theoretical approach is based on a variational principle stating the incremental equilibrium through the stationarity of a functional that could be defined as the incremental total potential energy. The analysis is carried out in two distinct phases: first a prediction of the behaviour of the structure subjected to an increment of load then a correction by means of Newton Raphson method of the results obtained in the previous incremental step. The approach makes it possible to determine the complete load deflection curve either in the prebuckling region or in the postbuckling one and to find out the critical load taking into account the deflection prior to buckling (non linearized buckling analysis).
12 citations
TL;DR: In this paper, the dynamics of rigid-viscoplastic bodies were discussed, bearing in mind large displacement effects, and extremal properties of the incremental solution of the dynamic problem were demonstrated.
Abstract: This paper discusses the dynamics of rigid-viscoplastic bodies, bearing in mind large displacement effects. The extremal properties of the incremental solution of the dynamic problem are demonstrated. It is shown that the true instantaneous acceleration field minimizes some quadratic functionals in a class of functions constrained by linear equations and inequalities.
11 citations
TL;DR: In this article, the incremental boundary value problem for rigid-viscoplastic isotropic continua subjected to dynamic actions is discussed and a pair of dual extremum theorems reduce the problem to the minimization of some functionals in a class of functions defined by appropriate constraints.
Abstract: The paper discusses the incremental boundary value problem for rigid-viscoplastic isotropic continua subjected to dynamic actions. A pair of dual extremum theorems reduces the problem to the minimization of some functionals in a class of functions defined by appropriate constraints. The first theorem takes as variables stresses and accelerations, the latter only the accelerations. Some conclusions end the paper.
10 citations
TL;DR: In this article, the inner flow and angular velocity of an infinite rotating disk are expressed in powers series of √t and the solution is established by expanding the velocity components and the pressure in powers of small time.
Abstract: The solution of unsteady forced flow against an unsteadily rotating disk is obtained when the outer flow and the angular velocity of the disk are expressed in powers series of √t. The solution is established by expanding the velocity components and the pressure in powers of small time. The extension of the obtained solutions is possible by using Zeytounian's technique. Finally, an analysis is made for the problem of the time-dependent flow due to an infinite rotating disk started accelerated from rest.
9 citations
TL;DR: In this paper, a suitable version of the local equivalence principle (basic for the construction of general relativity) and the principle of material (frame) indifference, divided into a translational part and a rotational part, is considered.
Abstract: In terms of classical physics and in connection with constitutive equations, a suitable version of the local equivalence principle (basic for the construction of general relativity) and the principle of material (frame) indifference, divided into a translational part and a rotational part, is considered.
7 citations
TL;DR: The limit analysis of indefinite plates resting on a continuous elastoplastic medium and subjected to a load distributed over a partial surface with a circular boundary yields the fundamental equation governing the problem as discussed by the authors.
Abstract: The limit analysis of indefinite plates resting on a continuous elastoplastic medium and subjected to a load distributed over a partial surface with a circular boundary yields the fundamental equation governing the problem. Minimum conditions are set and the solution that supplies the collapse load of the plate-soil system is found by variational calculus.
TL;DR: In this paper, the law governing the plastic collapse of plates is formulated on the basis of the well-known kinematic theorem of limit analysis, and a general procedure for the approximate determination of the collapse load is proposed.
Abstract: Rigid-plastic plates having a piecewise linear yield surface are studied by limit analysis. Extremum principles for the evaluation of specific dissipation power are defined by means of linear programming concepts. The law governing the plastic collapse of plates is formulated on the basis of the well-known kinematic theorem of limit analysis. A general procedure for the approximate determination of the collapse load is proposed. The paper ends with a brief numeric investigation of the uniformly loaded square plate.
TL;DR: In this article, the decay of vortices in the flow of a certain class of visco-elastic liquids (incompressible second-order fluids) is investigated.
Abstract: Decay of vortices in the flow of a certain class of visco-elastic liquids (incompressible second-order fluids) is investigated. It is found that in the flow of double array of vortices, the vortices decay much faster in such a liquid than in ordinary viscous liquids. For the flow in the wake of such a liquid past a two-dimensional grid, a pair of bound eddies occur behind the single elements of the grid as in the viscous case but their scale diminishes with increase in the elastic parameter.
TL;DR: In this article, a numerical solution for a fluid motion in a circular pipe orifice is compared with experimental results, and good agreement between the piezometric heads and head losses computed and those obtained in experiments is found.
Abstract: A numerical solution for a fluid motion in a circular pipe orifice is compared with experimental results. Knowledge of the velocity field allows us to find the pressure field. There is good agreement between the piezometric heads and head losses computed and those obtained in experiments.
TL;DR: In this article, the authors considered the limit state behavior of plates resting on an elastoplastic continuum subject to distributed loads and showed that the results are suitable for following the load carrying capacity of plates and the relative collapse mechanism as the limit resistance of the soil and the spread of the load acting on it vary.
Abstract: With reference to a theory expounded in a previous note [2] on the limit state behaviour of plates resting on an elastoplastic continuum subject to distributed loads, probable collapse mechanisms are considered in order to supplying more tractable solutions for technical practice. As the case is a general one, it is shown that the results obtained are suitable for following the load carrying capacity of plates and the relative collapse mechanism as the limit resistance of the soil and the spread of the load acting on it vary.
TL;DR: In this paper, a tensorial formulation of monoenergetic neutron diffusion theory is presented as can be derived starting from the integral form of the Boltzmann equation, whose components are functions of both the position and the properties of the material the body is made of.
Abstract: In this paper a tensorial formulation of monoenergetic neutron diffusion theory is presented as can be derived starting from the integral form of the Boltzmann equation. A result of this tensorial approach is that, as a consequence of a spatial variation of the macroscopic cross sections or of the finite dimensions of the body under examination, the diffusion coefficient is no longer a constant scalar quantity, but a second order symmetric tensor, whose components are functions of both the position and the properties of the material the body is made of. The components of the diffusion coefficient tensor are explicitly evaluated in the case of some homogeneous convex bodies.
TL;DR: In this paper, the author gives a general and unified treatment of first order phase equilibria for "classical bodies" like those considered by Truesdell and Toupin.
Abstract: In this note the Author gives a general and unified treatment of first order phase equilibria for “classical bodies” like those considered by Truesdell and Toupin in[3].
TL;DR: In this article, the problem of probabilistic minimum weight limit design is formulated as a stochastic programming problem and an algorithm is proposed and illustrated for the case of pin-jointed structures with two random continuous variables.
Abstract: The problem of probabilistic minimum weight limit design is formulated as a stochastic programming problem. The theoretical treatment considers monodimensional structures, geometrical parameters and integer design variables. An algorithm is proposed and illustrated for the case of pin-jointed structures with two random continuous variables. The paper follows previous researches of the Authors in the field of probabilistic approach to structural safety [29 ÷ 33].
TL;DR: In this paper, the concepts introduced in an earlier work with regard to one-degree-of-freedom, non-linear structural systems are extended to systems with "N" degrees of freedom and "Two" independent loading parameters.
Abstract: Some of the concepts introduced in an earlier work with regard to one-degree-of-freedom, non-linear structural systems are extended to systems with “N” degrees of freedom and “two” independent loading parameters.
TL;DR: In this paper, the restrictions on the mechanical and thermal constitutive equations of an elastic isotropic material were studied to ensure the local stability under suitable perturbations of the gradient of deformation and the temperature field of the fundamental state.
Abstract: The paper studies the restrictions on the mechanical and thermal constitutive equations of an elastic isotropic material, in order to ensure the local stability under suitable perturbations of the gradient of deformation and the temperature field of the fundamental state.
TL;DR: In this article, a procedure for calculating the natural frequencies and the principal modes of rotating helicopter blades based on the transfer matrix method is described, where the blade is divided into a finite number of elements considered as continuous.
Abstract: A procedure for calculating the natural frequencies and the principal modes of rotating helicopter blades based on the transfer matrix method is described. The blade is divided into a finite number of elements considered as continuous. A solution involving less laborious calculation, in which the masses are assumed to be concentrated, is also supplied.
TL;DR: In this paper, a method of computing the shear stress in a laminar boundary-layer without pressure gradient is described, where the non linear term in the Von Mises' equation is replaced by a suitable function; the resulting equation is the well known heat conduction equation, which can be solved in close form to give the wall stress on the wall.
Abstract: A method of computing the shear stress in a laminar boundary-layer without pressure gradient is described. The non linear term in the Von Mises' equation is replaced by a suitable function; the resulting equation is the well known heat conduction equation, which can be solved in close form to give the shear stress on the wall. The linearizing function is then determined for the Blasius problem by comparison with the known exact solution; it turns out that this function does not depend on the initial conditions but only on the local values of the skin friction. Assuming that this property is valid in general, the skin friction downstream of arbitrary velocity profiles can be easily computed. The method is then extended to the case of compressible flow and to the computation of the adiabatic wall temperature downstream of arbitrary temperature profiles. Several numerical examples are presented; the comparison with the exact numerical solutions shows very good agreement.
TL;DR: In this paper, the problem of characterising the dynamics of randomly excited systems is examined, and the direct method of Axelby is recalled and applied to a nonlinear system with random excitation characterised by a statistic of great interest in real physical systems.
Abstract: The problem of characterising the dynamics of randomly excited systems is examined. It is shown that the probability approach, though conceptually more rigorous, is difficult to apply to statistics other than normal ones. The direct method of Axelby is recalled and applied to a nonlinear system with random excitation characterised by a statistic of great interest in real physical systems. The application is developed parametrically with reference to a second order system for which the calculations are developed and the quantitative results discussed.
TL;DR: In this article, the state of stress from internal pressure in a nuclear reactor pressure vessel was examined using photoelastic models and the results were compared with those obtained from Eringen theoretical analysis.
Abstract: The state of stress from internal pressure in a nuclear reactor pressure vessel was examined using photoelastic models. The results were compared with those obtained from Eringen theoretical analysis. The Poisson ratio effect was investigated with reference to a cylinder-sphere junction. The results were also compared with photoelastic results for similar dimensions and with the values of a numerical analysis with finite element method of other authors.