Showing papers in "Meccanica in 1968"
TL;DR: In this paper, the problem of the deviation from the linear elastic, of the response of a nonlinear discrete structure to given loads, is formulated for various classes of cases, and all the problems considered are shown to be reducible to a single mathematical model: the quadratic program with sign constraints only.
Abstract: The search for the deviation from the linear elastic, of the response of a nonlinear discrete structure to given loads, is formulated for various classes of cases. All the problems considered are shown to be reducible to a single mathematical model: the quadratic program with sign constraints only. The Kubn-Tucker theorem for quadratic programming directly supplies the appropriate extremum principles, for which some physical interpretations are proposed. Other results of quadratic programming theory prove to be useful in the discussion of the structural problems considered.
126 citations
TL;DR: In this article, it was shown that the analysis problem in terms of finite (not incremental) stresses, is amenable to the Kuhn-Tucker conditions of a quadratic program.
Abstract: For elastic perfectly plastic discretized structures acted upon by given loads and dislocations, it is shown, under holonomic constitutive laws or no local unloading hypothesis, that the formulation of the analysis problem in terms of finite (not incremental) stresses, is amenable to the Kuhn-Tucker conditions of a quadratic program. Then it is readily derived a generalized form of the principle of Haar and Karman, together with an extremum theorem for displacements and plastic strains, which is the dual of the preceding one. As special cases of this theorems known variational principles follow, which thus turn out to be related in pairs by the duality notion as understood in programming theory. Also the statical and kinematical theorems of limit analysis are proved by means of the unitary conceptual framework supplied by quadratic programming.
105 citations
TL;DR: In this paper, two model struts subject to an axial force and to radiant heat parallel to the axis are studied dynamically, and the elastic and thermal deformations of the strut are lumped in one or two cells; the heat absorbed by each cell and the consequential thermal deformation depend on its rotation.
Abstract: Two model struts subject to an axial force and to radiant heat parallel to the axis are studied dynamically. The elastic and thermal deformations of the strut are “lumped” in one or two cells; the heat absorbed by each cell and the consequential thermal deformation depend on its rotation. Thermal inertia is neglected, while a viscous damping is introduced.
26 citations
TL;DR: In this article, the collapse theorems for materials which do not exhibit normality of the strain rate vector to the yield surface in the superposed stress and strain rate spaces are considered.
Abstract: The paper discusses the collapse theorems for materials which do not exhibit normality of the strain rate vector to the yield surface in the superposed stress and strain rate spaces. The consequences of the lack of normality on the designs for minimum weight are considered.
20 citations
TL;DR: In this paper, the diffraction of a plane wave incident on an isolated breakwater is studied, and the exact solution of the problem is briefly reported and a general method involving energies is used to determine comparative importance of the terms of the series which appear in the solution, which becomes of much greater facility in use in practical problems.
Abstract: The diffraction of a plane wave incident on an isolated breakwater is here studied: the exact solution of the problem is briefly reported and a general method involving energies is used to determine comparative importance of the terms of the series which appear in the solution, which becomes of much greater facility in use in practical problems. Numerical calculations have been carried out for twelve different cases, with the wavelength of the incident wave comparable to the length of the breakwater. Results are graphically shown in a set of tables.
15 citations
TL;DR: In this article, the behavior of the beam-soil system is examined within the scope of the bilateral schematization of ideal elastoplastic bodies, in the following work stages; the expression for the limit load is supplied for each stage: the elastic unloading of the material, and the successive propagation of plastification in the soil which, being related to the displacement of the hinges in the beam, leads to the identification of the collapse mechanism of the systme.
Abstract: The behavior of the beam-soil system is examined within the scope of the bilateral schematization of ideal elastoplastic bodies, in the following work stages; the expression for the limit load is supplied for each stage:
Two peculiar features of the problem are highlighted:1) the “plastic hinge migration” phenomenon, due to the elastic unloading of the material, and2) the successive propagation of plastification in the soil which, being related to the displacement of the hinges in the beam, leads to the identification of the collapse mechanism of the systme.
14 citations
TL;DR: In this paper, the effects of a uniform rotation on the propagation of small perturbations through an anisotropic collisionless plasma are investigated and the effects are present in various ways on the well-known "hose", "mirror" and gravitational instabilities.
Abstract: The effects of a uniform rotation on the propagation of small perturbations through an anisotropic collisionless plasma are investigated. These effects are present in various ways on the well-known “hose”, “mirror” and gravitational instabilities. In Part I we consider plane perturbations, in Part II cylindrical. Some remarks about stability and hydromagnetic waves in an anisotropic collisionless plasma are given in Appendix.
13 citations
TL;DR: A geometrical characterisation for externally pressurized journal bearings having been defined, the relationship between geometry and dynamic behaviour is investigated systematically in the present paper as mentioned in this paper, the result of the investigation is a set of diagrams covering cases of practical interest not presented to such an extent before.
Abstract: A geometrical characterisation for externally pressurized journal bearings having been defined, the relationship between geometry and dynamic behaviour is investigated systematically in the present paper. The result of the investigation is a set of diagrams covering cases of practical interest not presented to such an extent before.
9 citations
TL;DR: In this paper, the buckling behavior of three-hinged arches in the inelastic range has been illustrated by a bilinear stress-strain relationship in the deformable elements.
Abstract: In analogy with the well-known Shanley's column model, a model has been devised to illustrate the buckling behaviour of three-hinged arches in the inelastic range. A bilinear stress-strain relationship has been assumed in the deformable elements. As in the case of the compressed strut, a wholesegment of bifurcation is found, and load values analogous to thetangent modulus (Shanley) andreduced modulus (Karman) loads can be defined. An example of load-displacement curves is fully developed.
7 citations
TL;DR: In this paper, the authors proposed formulas, having the same general validity, whereby the quasi-plane stress system in rotating discs may be described in terms of absolutely convergent hypergeometric series.
Abstract: On the basis of a general relation — capable of expressing analytically the thickness law for a wide range of rotating discs of different shapes — the Author proposes formulas, having the same general validity, whereby the quasi-plane stress system in such discs may be described in terms of absolutely convergent hypergeometric series.
7 citations
TL;DR: In this paper, the effect of vanishing viscous damping on the stability of non-conservative linear elastic systems is studied, with special reference to systems that lose stability statically through the emergence of new equilibrium configurations close to the principal one, i.e. by divergence.
Abstract: A study of the effect of vanishing viscous damping on the stability of nonconservative linear elastic systems, with special reference to systems that lose stability statically through the emergence of new equilibrium configurations close to the principal one, i. e. by divergence. It is shown that in this case slight damping presents a wide range of effects on the stability of the system.
TL;DR: In this article, the limit analysis of three-dimensional rigid-perfectly plastic continua with associated flow-law (standard materials) is discussed and some approximate procedures which follow from Mura-Lee variational method and from upper and lower bound theorems are presented.
Abstract: The paper discusses the limit-analysis of three-dimensional rigid-perfectly plastic continua with associated flow-law (standard materials) It presents some approximate procedures which follow from Mura-Lee variational method and from upper and lower bound theorems
TL;DR: In this article, an elastoplastic beam-column model with one degree of freedom subjected statically to an on-center or off-center axial compressive force is considered, resulting from a transverse periodic acting force in resonance with the structure in the elastic range.
Abstract: An elastoplastic beam-column model with one degree of freedom subjected statically to an on-center or off-center axial compressive force is considered. Its dynamic behavior in the elastoplastic range, resulting from a transverse periodic acting force in resonance with the structure in the elastic range, is examined. The principal features are highlighted by a phase plane study.
TL;DR: In this paper, the first harmonic of a sinusoidal progressing wave is considered and only gravity waves are dealt with, surface tension effects being ignored, and only the gravity wave is dealt with.
Abstract: The first harmonic of a sinusoidal progressing wave is considered here. Only gravity waves are dealt with, surface tension effects being ignored.
TL;DR: In this article, a study of the response of a continuum to given loads is carried out assuming a piecewise linear yield locus, normality, noninteracting yield planes and linear strain bardening, and minimum properties for the plastic strain rates in the incremental case and for plastic strains satisfying holonomic and nonholonomic stress-strain laws.
Abstract: A study of the response of a continuum to given loads is carried out assuming a piecewise linear yield locus, normality, non-interacting yield planes and linear strain bardening. Minimum properties are determined for the plastic strain rates in the incremental case and for plastic strains satisfying holonomic and non-holonomic stress-strain laws, thus extending to continua the minimum properties determined elsewhere for discrete structural linear hardening systems.
TL;DR: In this article, a supersonic molecular beam production system is described in which a continuous flux of Argon molecules can be produced as high as 4 · 1018 molecules sterad−1 sec−1 in a vessel where the background pressure can be kept below 10−6 mmHg using relatively little cryo and diffusion pumping facilities.
Abstract: A supersonic molecular beam production system is described in which a continuous flux of Argon molecules can be produced as high as4 · 10
18 molecules sterad−1 sec−1 in a vessel where the background pressure can be kept below10
−6 mmHg using relatively little cryo and diffusion pumping facilities. The beam intensity is measured at different stagnation pressures as a function of nozzle-skimmer separation and skimmer diameter. The results are compared with the existing theories, and information is obtained on the radial temperature distribution in the free expanding jet.
TL;DR: In this article, the algebraic condition ensuring the validity of Hadamard's criterion of local stability in a Prandtl-Reuss solid is examined and four fundamental situations depending on the possible transitions of state are considered.
Abstract: The algebraic condition ensuring the validity of Hadamard's criterion of local stability in a Prandtl-Reuss solid is examined. Four fundamental situations depending on the possible transitions of state are considered.
TL;DR: In this paper, the thermodynamic foundations of a theory of permanent deformations are considered: in the axioms, an appropriate definition of free enthalpy plays an essential role.
Abstract: The thermodynamic foundations of a theory of permanent deformations are considered: in the axioms, an appropriate definition of free enthalpy plays an essential role. Our developments are parallel (but in a certain sense dual) to those which occur in a theory of viscoelastic materials, due to Coleman and Noll.
TL;DR: In this paper, a uniqueness theorem and an existence theorem for motions asymptotically stable in the mean and periodically depending on time, are demonstrated in magnetohydrodynamics.
Abstract: A uniqueness theorem and an existence theorem for motions asymptotically stable in the mean and periodically depending on time, are demonstrated in magnetohydrodynamics, on the hypothesis that a motion sufficiently regular and asymptotically stable in the mean exists. In particular, similar theorems for steady motions are deduced. The procedure used is also a simple method for constructing periodic and steady motions.
TL;DR: In this paper, it was shown that there exist at least two different solutions of the problem of concentrated loads in the two-dimensional, linear couple-stress theory when the formulation is based on the usual uniqueness theorem.
Abstract: It is pointed out that there exist at least two different solutions of the problem of concentrated loads in the two-dimensional, linear couple-stress theory when the formulation is based on the usual uniqueness theorem. An extension of this uniqueness theorem is proved. A set of conditions sufficient for uniqueness is found and is used in a formulation of the concentrated load problem which results in a unique solution. The significant new condition is that the order of the stress singularity is limited to O(r−1), where r is the distance from the concentrated load.
TL;DR: In this article, a differential equation for the minors of the state transition matrix of linear time-invariant systems is established, and an example is presented, where the differential equation is employed in order to check the existence of the extremal control of a linear system with a performance index given by the integral of a quadratic form.
Abstract: A differential equation for the minors of the state transition matrix of linear time-invariant systems is established. An example is then presented, where the differential equation is employed in order to check the existence of the extremal control of a linear system with a performance index given by the integral of a quadratic form.
TL;DR: In this paper, the authors present the solutions to several plate bending problems as governed by a recent theory developed by Green and Naghdi, into which couple-stress is incorporated.
Abstract: Presented in this paper are the solutions to several plate bending problems as governed by a recent theory developed by Green and Naghdi, into which couple-stress is incorporated. Specifically, each problem considered is subjected to boundary conditions emanating from a singular load distribution acting on the free edge of a semi-infinite plate. The method of integral transforms is applied in the solutions. In general, it is found that the singularities in the shear and moment resultants are of the same order as those given in Reissner's plate theory, however the detailed structures of these singular functions are altered. The present theory also suggests that, in most cases, the maximum magnitudes of the moment resultants are diminished as compared to the corresponding results given in Reissner's theory. Also discussed is the exact relationship between the Green-Naghdi theory and Reissner's theory.
TL;DR: In this article, the nature of a material is in large part described by its symmetry group, and it is proposed to extend this concept to a more general type of symmetry transformation, and the use of such an extension is illustrated by using it to define several classes of materials and presenting the corresponding representation theorems.
Abstract: The nature of a material is in large part described by its symmetry group. It is proposed to extend this concept to a more general type of symmetry transformation, and the use of such an extension is illustrated by using it to define several classes of materials and presenting the corresponding representation theorems.
TL;DR: In this article, a solution for a particular plane flow (with zero hydraulic slope) is carried out, supposing that the components of the stress tensor T are polynomials in the component of the deformation rate tensor F.
Abstract: After a few basic remarks on continuous media mechanics, equations of unsteady laminar flow for non-newtonian incompressible fluids are written; a solution for a particular plane flow (with zero hydraulic slope) is carried out, supposing that the components of the stress tensor T are polynomials in the components of the deformation rate tensor F. In particular if we adopt a cubic law, we recognize a second viscosity coefficient, which may be a positive or negative number; a way is then suggested for finding experimentally both viscosity coefficients of the fluid; a simple numerical example is also given.
TL;DR: In this article, the problem of motion of a conductive, homogeneous and isotropic elastic body subjected not only to externally applied mass forces and surface forces, but also to a uniform magnetic field, in which an induced magnetic field is generated, is reduced to the consideration of a single differential vector equation in which the displacement of a point in the elastic body is the only unknown.
Abstract: This paper deals first with the equations of motion of a conductive, homogeneous and isotropic elastic body subjected not only to externally applied mass forces and surface forces, but also to a uniform magnetic field, in which an induced magnetic field is generated. On the assumption that the electrical conductivity is infinite, the problem of motion is reduced to the consideration of a single differential vector equation in which the displacement of a point in the elastic body is the only unknown. The conditions that must be satisfied at the surface are then considered. Using the generalised formula of Kirchhoff, formulas expressing the Cartesian components of the displacement, the cubic dilatation and the rotation components are established by means of the so-called fundamental elements.
TL;DR: In this paper, the steady-state stress and displacement fields arising in an indefinite, elliptically-holed cilindrical body containing a line heat source were examined and some numerical results were given for this as well as for the case of hole with a constant-temperature surface.
Abstract: A report on the steady-state stress and displacement fields arising in an indefinite, elliptically-holed cilindrical body containing a line heat source. The case of an adiabatically-walled hole is examined and some numerical results are given for this as well as for the case of hole with a constant-temperature surface.
TL;DR: In this paper, the amplitude of linear vibrations of a slightly unbalanced shaft, rotating on lubricated bearings near one of its critical speeds, is determined, taking into account the damping action of lubricant forces and couples on the journal movement.
Abstract: Amplitudes of linear vibrations of a slightly unbalanced shaft, rotating on lubricated bearings near one of its critical speeds, are determined, taking into account the damping action of lubricant forces and couples on the journal movement. The analysis (carried out on the lines of earlier work by Sternlicht, Warner and others) shows that the effect of lubricant couples is never relevant in the normal range of variability of parameters. The analysis puts instead in evidence the effect of the total damping action of the lubricant and hence the importance in design of forecasts of amplitude of vibration at running speed. The attention s often limited to forecasts of critical speeds; such procedure may be misleading particularly near higher critical speeds.
TL;DR: In this article, it is shown that the momenta are constructed tensorially only with the two fundamental tensors of the hypersurface since Dirac's velocities are equated with the components of the second fundamental tensor.
Abstract: In the Hamiltonian formulation of relativistic theory of gravitation the gravitational field at a given time is defined on a spacelike hypersurface of Riemannian space-time by six gravitational potentials and as many conjugate momenta. The former characterize the metric of the hypersurface and it is shown that the momenta are constructed tensorially only with the two fundamental tensors of the hypersurface since Dirac's velocities are equated with the components of the second fundamental tensor. Invariants of the two fundamental tensors, geometrically interpretable, can then be introduced into the Hamiltonian. It is at once clear from the Gauss and Codazzi equations, relating the two fundamental tensors of a hypersurface that the four secondary constraints, which the conjugate dynamical variables satisfy, are equivalent to four Einstein gravitational equations.
TL;DR: In this article, the displacement components of the orthotropic media are integrated with operational methods by separation of the variables and the process leads to a symbolic solution of the problem from which the resolvent equations in the form of power series of operators are constructed.
Abstract: Equilibrium equations for orthotropic media are written taking the displacement components as unknowns; these equations are integrated with operational methods by separation of the variables. The unknown quantities are six « initial funcitons » that is, displacements and their partial derivatives with respect toz, calculated on the planez=0. Following a method of structural mechanics, the cases of symmetrical and nonsymmetrical loading of plate, namely compression and flexion, are considered separately. The separation of the variables allows us to resolve in two successive stages the problem of the boundary conditions: the Cauchy conditions on the surfacesz=± h become differential equations to which we associate the condition on the cylindrical surface. The process leads to a symbolic solution of the problem from which we construct the resolvent equations in the form of power series of operators. If terms of a higher order are retained in these equations, a more accurate theory is obtained; it is shown that if only the first term is assumed, the equation for the ortho tropic plate in the Kirchhoff-Love sense is obtained. The method is applied in order to resolve a problem numerically; the results are compared with those deduced by the usual theory.
TL;DR: In this paper, the motion of a rigid body, with variable mass, free in space is considered, starting from the Eulerian differential equations, which are modified in relation to the variability of the mass and of the principal moments of inertia.
Abstract: The problem of the motion of a rigid body, with variable mass, free in space is considered. The problem is studied starting from the Eulerian differential equations, which are modified in relation to the variability of the mass and of the principal moments of inertia.