A development on plastic work methods for determining the plastic load for mechanical components and structures

A method for determining plastic collapse loads of mechanical components and structures on the basis of two linear elastic finite element analysis is presented in this paper. The r-nodes, which are essentially statically determinate locations, are obtained by GLOSS analysis. The plastic collapse loads are determined for statically determinate and indeterminate components and structures by using the single-bar and the multibar models, respectively. The paper also attempts to unify the concepts of load-control, limit load, reference stress and stress-classification. The GLOSS R-Node method is applied to several component configurations of practical interest.

One of the major obstacles that are limiting the development of deployable integrated sensing and actuation solutions is the scarcity of power. Converted energy from ambient loading in civil and mechanical structures is typically used as an alternative solution. Although, piezoelectric vibration harvesters have been widely used, these elements exhibit a narrow natural frequency response range, thus considerably limiting the levels of harvestable power. Most of the previously used methods focus only on modifying the transducer’s properties and configurations. These techniques do little to modify the stimuli from the source. In contrast, this work proposes to focus on the input signal generated within the structure by inducing amplified response amplitude and a frequency up-conversion toward the harvesters’ natural response spectrum. This paper introduces the concept of using mechanically-equivalent frequency modulators that can transform the low-amplitude and low-rate service and ambient deformations into an amplified input to the piezoelectric transducer. The introduced methods will allow energy generation and conversion for loads within the unexplored quasi-static frequency range (<< 1 Hz). The post-buckling behavior of bilaterally restrained columns and bistable plates is used for frequency up-conversion. A bimorph cantilever PVDF piezoelectric beam, attached to the columns and plates, are used for energy conversion. Experimental prototypes were built and tested to validate the introduced concept. The levels of extractable power are evaluated for different cases under varying input frequencies. Finally, numerical simulations provide insight into the scalability and performance of the developed concepts.

Converted energy from ambient loading in civil and mechanical structures is typically used as a viable alternative. Although, piezoelectric vibration harvesters have been widely used given their energy conversion ability, these elements exhibit a narrow natural frequency response range, thus considerably limiting the levels of harvestable power. Recently our group has introduced the concept of using mechanically-equivalent frequency modulators that can transform the low-amplitude and low-rate service and ambient deformations into an amplified input to the piezoelectric transducer. The introduced methods allow energy generation and conversion within the unexplored quasi-static frequency range (≪ 1 Hz). The post-buckling behavior of bilaterally constrained columns was used for frequency up-conversion, and piezoelectric cantilever beams, attached to the columns, were used for energy conversion. The introduced concept was experimentally validated and finite element simulations were developed to evaluate the effect of system parameters (stiffness, thickness, and walls gap) on the position of the snap-through transition events and the levels of force-displacement at the multiple-equilibrium configurations. It was shown that the considered system parameters can determine the absolute levels of force and displacement, but they offer limited control on the number and the relative spacing between the energy-drop events. This paper shows that the combination of multiple slender elastic columns modulators, in parallel configurations, allows for the tailoring of the number and magnitude of the mode branch switching during the postbuckling response of the complete system. Experimental and numerical results are presented to validate the proposed concept.

The all-optical fiber-based intelligent sensing system is one key technology for acoustic/ultrasonic structural health monitoring. Damages such as cracking or impact loading in civil, aerospace, and mechanical structures can generate transient ultrasonic waves, which can reveal the structural health condition. Hence, there is a great need to develop a high precision adaptive sensor for large-value strain signals with large frequency range that can extent to several hundred kilohertz in ultrasonic/acoustic sensing. In this work, we explore an intelligent system based on a fiber Bragg grating (FBG) and an erbium-doped fiber amplifier (EDFA), composing as a fiber cavity that offers significant advantages and higher performance in ultrasonic/acoustic sensing applications. The ASE light emitted from the EDFA and reflected by a FBG is amplified in the fiber cavity and coupled out by a 90:10 coupler, which is demodulated by an unbalanced Mach-Zehnder interferometer (MZI) composed by a 2×2 coupler and a 3×3 coupler. As the reflective spectrum of the FBG sensor changes due to excited acoustic waves, the shift of the laser output wavelength is subsequently converted into a corresponding phase change. We theoretically and experimentally calculate the three output signals using a differential cross-multiplication (DCM) algorithm to directly demodulate the wavelength shift of the FBG sensor. The experimental results demonstrate that the proposed FBG acoustic sensing system has high sensitivity and can respond the ultrasonic waves into the hundreds of kilohertz frequency range, which shows a potential for acoustic emission detection in practical applications.

Limit loads for mechanical components and structures are determined in this paper by invoking the concept of equivalence of “static indeterminacy,” which relates a multidimensional pressure component configuration to a “reference two-bar structure.” Simple scaling relationships are developed that enable the rapid determination of limit loads. The reference two-bar structure method is applied to a number of pressure component configurations with or without notches.

An approximate method for determining limit loads of mechanical components and structures on the basis of two linear elastic finite element analyses is described. The load-control nature of the redistribution nodes (r-nodes) leads to considerable simplifications. The combined r-node equivalent stress, which can be obtained by invoking an appropriate multibar mode, can be identified with the reference stress. The method is applied to beam, framed and arched structures, and the limit load estimates obtained are reasonably accurate.

Limit loads for mechanical components and structures are determined in this paper by invoking the concept of equivalence of “static indeterminacy” that relates a multidimensional pressure component configuration to a “reference two-bar structure.” Simple scaling relationships are developed that enable the rapid determination of limit load multipliers. The reference two-bar structure method is applied to a number of pressure component configurations with or without notches.

The procedures described in this paper for determining a limit load is based on Mura’s extended variational formulation. Used in conjunction with linear elastic finite element analyses, the approach provides a robust method to estimate limit loads of mechanical components and structures. The secant modulus of the various elements in a finite element discretization scheme is prescribed in order to simulate the distributed effect of the plastic flow parameter, μ0. The upper and lower-bound multipliers m0 and m′ obtained using this formulation converge to near exact values. By using the notion of “leap-frogging” to limit state, an improved lower-bound multiplier, mα, can be obtained. The condition for which mα is a reasonable lower bound is discussed in this paper. The method is applied to component configurations such as cylinder, torispherical head, indeterminate beam, and a cracked specimen.

The transient loading of mechanical components and structures is usually performed with the assumption that there are no preloads applied to them since preloads are usually small and can be neglected. However, for certain structures used in the nuclear power industry, the preloads are significant and must be considered in the transient analysis. Two examples of these types of structures are prestressed concrete containments and inter-compartment locks, which respond with both geometric and material nonlinearities during transient loadings. An efficient computational engine is presented in this paper for the solution of these types of problems. An example is presented to illustrate the algorithm. A preloaded platen, which is part of an inter-compartment lock, is subjected to an impulsive load. The resulting transient response of the system is presented.

The purpose of this study is to investigate the effects of hole/holes on stress concentrations in a plate using a current industry standard software - Finite Element Analysis (FEA). Plate with hole/holes is a common engineering application such as in automobile, marine, aerospace and mechanical structures. Hole/Holes can be seen in many thin-walled mechanical and automobile structures and components. For example, hole/holes are found in residential/commercial buildings’ steel structural studs to allow plumbing installation, web or flange of steel box girders in bridges is furnished with holes to ease inspection works, electrical and heating conduits in the walls or ceilings and ribs attached to the main spar of an aeroplane’s wing are frequently come with holes. These hole/holes are one type of discontinuities within the structure (e.g. thin plate) that leads to changes in elastic stiffness and may tend to failures. Proper knowledge of stresses, strains, deflection and stress concentration (SC) are required to design any structures. In the geometry of the plate, under different loading, stress concentration rises from any abrupt change. And due to this, throughout the cross-section, the uniform stress distribution does not occur. At a point of stress concentration, as a results failures like fatigue cracking and plastic deformation commonly occur. Hence, it is very important in any engineering structural design to know about the stress concentration on plates with holes. In the present study stress concentration in a plate with a circular central hole and offset hole subjected to uniaxial loading (axial tension) is calculated using Finite Element of Analysis (FEA). Equations of SCF given by Peterson are dependent on three parameters namely, hole radius (a), distance from the bottom edge to the centre of hole (c) and distance from top edge to centre of hole (e). By varying either ‘c’ or ‘e’ or the ratio of ‘e/c’, an effort is made to study stress concentration factors for the determination of the edge effect by varying the hole to edge distance. The results show that von Mises stresses increased with increasing ‘e/c’ or ‘a/c’, which in turn increases SCF and finally leads to failure.

In this paper, a nonlinear numerical technique is developed to calculate the limit load and failure mode of structures obeying an ellipsoid yield criterion by means of the kinematic limit theorem, nonlinear programming theory and displacement-based finite element method. Using an associated flow rule, a general yield criterion expressed by an ellipsoid equation can be directly introduced into the kinematic theorem of limit analysis. The yield surface is not linearized and instead a nonlinear purely kinematic formulation is obtained. The nonlinear formulation has a smaller number of constraints and requires less computational effort than a linear formulation. By applying the finite element method, the kinematic limit analysis with an ellipsoid yield criterion is formulated as a nonlinear mathematical programming problem subject to only a small number of equality constraints. The objective function corresponds to the dissipation power which is to be minimized and an upper bound to the plastic limit load of a structure can then be calculated by solving the minimum optimization problem. An effective, direct iterative algorithm has been developed to solve the resulting nonlinear programming formulation. The calculation is based purely on kinematically admissible velocities. The stress field does not need to be calculated and the failure mode of structures can be obtained. The proposed method can be used to calculate the bearing capacity of clay soils in a direct way. Some examples are given to illustrate the validity and effectiveness of the proposed method.

An adaptive selective ES-FEM for plastic collapse analysis

The gross plastic deformation and associated plastic loads of four axisymmetric torispherical pressure vessels are determined by two criteria of plastic collapse: the ASME twice elastic slope (TES) criterion and the recently proposed plastic work curvature (PWC) criterion. Finite element analysis was performed assuming small and large deformation theory and elastic-perfectly plastic and bilinear kinematic hardening material models. Two plastic collapse modes are identified: bending-dominated plastic collapse of the knuckle region in small deformation models and membrane-dominated plastic collapse of the cylinder or domed end in large deformation models. In both circumstances, the PWC criterion indicates that a plastic hinge bending mechanism leads to gross plastic deformation and is used as a parameter to identify the respective plastic loads. The results of the analyses also show that the PWC criterion leads to higher design loads for strain hardening structures than the TES criterion, as it takes account of the effect of strain hardening on the evolution of the gross plastic deformation mechanism.

The r-nodes (redistribution nodes) are locations in mechanical components and structures that are load-controlled, and therefore insensitive to material constitutive relationships. These locations and their respective equivalent stress values can be approximately determined on the basis of two linear elastic analyses. By invoking equilibrium considerations, a simple relationship can be established between the “combined r-node equivalent stress” and the plastic collapse loads. On account of its load-controlled nature, the combined r-node equivalent stress can be identified with the reference stress, which is extensively used in carrying out pressure component integrity assessments. The concept of r-nodes is also related to the primary stresses in pressure components, and in designing mechanical components and structures for minimum weight. This paper proposes simple phenomenological models in an attempt to characterize the functioning of r-nodes.

The judgments of lawyers on the mechanism of human rights protection are considered. The analysis of the existing approaches in modern legal science to determining the structure of the mechanism of human rights protection showed an insufficiently complete description of its elemental composition. The chosen theoretical tools, consisting of worldview dialectical and anthropological approaches, structural-functional method and other methods of cognition, allowed to clarify the internal structure of the mechanism of human rights protection, as well as the functional purpose of each of its constituent elements. A theoretical model of the structure of the studied phenomenon of state and legal reality is proposed. The first component is defined as subject-ideological, which includes subjects of law enforcement (judicial and law enforcement agencies and human rights institutions) in conjunction with the inherent in these subjects of professional legal consciousness and legal culture. The second is the instrumental-functional component, which includes legal means aimed at preventing violations of human rights and freedoms; cessation of illegal behavior; restoration of the violated right and bringing the perpetrators to justice, as well as measures to ensure the proceedings in cases of administrative offenses and prevent the avoidance of criminal liability. Logically, this component also includes law enforcement and human rights activities and law enforcement and human rights relations, respectively, in the process and within which these remedies are implemented. The third component of the human rights mechanism is communicative, which includes structural links that ensure its integrity and unity, as well as functional links that ensure its effectiveness. Keywords: human rights protection mechanism, structure of human rights protection mechanism, subject-ideological component, instrumental-functional component, communicative component.