Equilibrium equations for 3D critical buckling of helical springs

In most cases, the research on the buckling of a helical spring is based on the column, the spring is equivalent to the column, and the torsion around the axial line is ignored. A three-dimensional （3D） helical spring model is considered in this paper. The equilibrium equations are established by introducing two coordinate systems, the Frenet and the principal axis coordinate systems, to describe the spatial deformation of the center line and the torsion of the cross section of the spring, respectively. By using a small deformation assumption, the variables of the deflection can be expanded into Taylor＇s series, and the terms of high orders are ignored. Hence, the equations can be simplified to the functions of the twist angle and the arc length, which can be solved by a numerical method. The reaction loads of the spring caused by the axial load subjected to the center point are also discussed, giving the boundary conditions for the＇solution to the equilibrium equations. The present work is useful to the research on the behavior of the post-buckling of the compressed helical spring.

A NEW SOLUTION TO STRUCTURAL FUZZY FINITE ELEMENT EQUILIBRIUM EQUATIONS (SFFEEE)

A speedy accurate solution to structural fuzzy finite element equilibrium equations (SFFEEE), by combining the definition of the solution of interval equations with the mechanical meaning of the structural finite element equilibrium equations (SFEEE), was put forward. The fuzzification of the SFFEEE, which is discussed in this paper, originates from that of material property, structural boundary conditions and external loading. The computing quantity of this solution is almost equal to that of the general finite element method (GFEM).

NEW SCALAR-TYPE EQUILIBRIUM EQUATIONS OF THE GENERAL SPACE FORCE SYSTEM

Using the principle of analytical geometry, several properties of the space straight lille are proved. Based on these properties, the equilibrium of general space force system is considered and its four new scalar-type equilibrium equations are derived which are equivalent to the vector-type necessary and sufficient conditions far equilibrium.

METHOD OF EQUILIBRIUM DIFFERENTIAL EQUATION FOR ANALYSIS OF STRENGTH OF LARGE DEFLECTION DRILL STRING

To counter the strength problem of drill string in well of large curvature and small diameter, well axis was taken as datum mis. Based on description of deflection of well an's and on analysis of three dimensional forces of a small section of drill string, equilibrium differential equations of large deflection drill string were established. The internal forces were found by Longe-Kutta method. The stresses were found by using them and the strength prerequisite was established. Stresses of drill string in lateral horizontal well H767 were computed. The results are in agreement with those of finite element model and soft-rope rigidified model. But the method is simpler for computation than finite element model and is more perfect than soft-rope rigidified model. Curvature of the well is too large and there is stress concentration so that the fraction accident of drill string occurs.

GIS-based 3D limit equilibrium analysis for design optimization of a 600 m high slope in an open pit mine

Combining the GIS （geographic information systems） grid-based data with four proposed column-based 3D slope stability analysis models, a comprehensive solution of a high-steep open-pit slope has been obtained. For six searching ranges, 19 critical slip surfaces of different sizes have been studied, in which the minimum 3D safety factor is 1.33. Comparison of 3D safety factors of designed and proposed slope plans shows for all the critical slip surfaces for the proposed plan, the smallest 3D safety factor is 1.33 under the most unfavorable condition. This means that the proposed plan of the high slopes, about 600 m, of an open pit （2-5° steeper than designed plan） is feasible.

Thermodynamic theory of flotation for a complex multiphase solid -liquid system and high-entropy flotation

The flotation of complex solid–liquid multiphase systems involve interactions among multiple components,the core problem facing flotation theory.Meanwhile,the combined use of multicomponent flotation reagents to improve mineral flotation has become an important issue in studies on the efficient use of refractory mineral resources.However,studying the flotation of complex solid–liquid systems is extremely difficult,and no systematic theory has been developed to date.In addition,the physical mechanism associated with combining reagents to improve the flotation effect has not been unified,which limits the development of flotation theory and the progress of flotation technology.In this study,we applied theoretical thermodynamics to a solid–liquid flotation system and used changes in the entropy and Gibbs free energy of the reagents adsorbed on the mineral surface to establish thermodynamic equilibrium equations that de-scribe interactions among various material components while also introducing adsorption equilibrium constants for the flotation reagents adsorbed on the mineral surface.The homogenization effect on the mineral surface in pulp solution was determined using the chemical potentials of the material components of the various mineral surfaces required to maintain balance.The flotation effect can be improved through synergy among multicomponent flotation reagents;its physical essence is the thermodynamic law that as the number of compon-ents of flotation reagents on the mineral surface increases,the surface adsorption entropy change increases,and the Gibbs free energy change of adsorption decreases.According to the results obtained using flotation thermodynamics theory,we established high-entropy flotation theory and a technical method in which increasing the types of flotation reagents adsorbed on the mineral surface,increasing the adsorption entropy change of the flotation reagents,decreasing the Gibbs free energy change,and improving the adsorption efficiency and stability of the flotation reagents improves refractory mineral flotation.

BASIC EQUATIONS OF THE PROBLEM OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE WITH VARIABLE THICKNESS

Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction),the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given;then introducing the dimensionless variables and three small parameters,the dimensionaless governing equations of the deflection function and stress function are given.

Compositions,Proportions,and Equilibrium Temperature of Coexisting Two-feldspar in Crystalline Rocks

Compositions, proportions, and equilibrium temperature of coexisting two-feldspar in crystalline rocks are of great importance to classification in petrography and interpretation of petrogenesis. Crystalline rocks are usually composed of 4-6 minerals （phases）, depending on their independent chemical components and the equilibrium temperature of crystallizations. In general, number of mineral phases can be determined by the ＂Phase Rule＂. According to the mass balance principle, bulk composition of coexisting two-feldspar could be evaluated from the bulk chemistry of a rock, provided that the compositions of the coexisting mafic mineral phases containing calcium, sodium, and potassium oxides are determined, e.g., by microprobe analysis. The compositions, proportions, and temperature of two-feldspar in equilibrium can thus be simultaneously resolved numerically from bulk composition of the rock, by incorporating the activity/composition relations of the ternary feldspars with the mass balance constraints. Upon the numerical approximation method presented in this paper, better-quality, internally consistent data on feldspar group could usually be obtained, which would be expected more realistic and accurate in consideration of thermodynamic equilibria in the system of crystalline rocks, as well as bulk chemistry of a rock and the composing minerals.

COORDINATES OF PRINCIPAL STRESSES FOR ELASTIC PLANE PROBLEM

In this paper, the equilibrium equations on orthogonal curve coordinates made of curves of principal stresses are disscused and their properties in process of solution are presented through a simple example. Therefore, it is deduced that there is another way to solve problems in elasticity, i.e., by assumption of orthogonal curves of principal stresses.

Seismic Analysis of Shear-Wall Structures with Vertically Installed Dampers

Shear-wall structures are quite common in seismic areas because of their successful seismic behavior during severe earthquakes. But shear walls are prone to brittle failure. This study proposes a new method of vertically installed dampers （VID） to reduce the vibration in shear-wall structures. The motion characteristic of a vertical damping system is that every mass has horizontal and rotational displacements simultaneously, The establishment of dynamic equations should take into account the equilibrium conditions of both horizontal and rotational vibrations. Dynamic equilibrium equations of VID systems are derived from a model of a structure with VID. An example shear-wall structure, with and with- out VID, is studied. There are some changes in the characteristics of the maximum horizontal displacement response. Without dampers, the relative displacements between different floors in the shear wall increase with height. With dampers, the relative displacements are more uniformly distributed, and lateral displacements at the top and at the bottom are closer. When the damping coefficient is 1 000 kN · s/ m, the numerical results reveal that the maximum horizontal displacement and the maximum rotational displacement of the top floor have reduced by 59.3 % and 54.8 % respectively.

Three-dimensional critical slip surface locating and slope stability assessment for lava lobe of Unzen volcano

Even Unzen volcano has been declared to be in a state of relative dormancy,the latest formed lava lobe No.11 now represents a potential slope failure mass based on the latest research.This paper concentrates on the stability of the lava lobe No.11 and its possible critical sliding mass.It proposes geographic information systems (GIS) based three-dimensional (3D) slope stability analysis models.It uses a 3D locating approach to identify the 3D critical slip surface and to analyze the 3D stability of the lava lobe No.11.At the same time,the new 3D approach shows the effectiveness in selecting the range of the Monte Carlo random variables and locating the critical slip surface in different parts of the lava lobe No.11.The results are very valuable for judging the stability of the lava lobe and assigning the monitoring equipments.

Static pressure redistribution mechanism of non-axisymmetric endwall based on radial equilibrium

Non-axisymmetric endwall contouring has been proved to be an effective flow control technique in turbomachinery.Several different flow control mechanisms and qualitative design strategies have been proposed.The endwall contouring mechanism based on the flow governing equations is significant for exploring the quantitative design strategies of the nonaxisymmetric endwall contouring.In this paper,the static pressure redistribution mechanism of endwall contouring was explained based on the radial equilibrium equation.A quantified expression of the static pressure redistribution mechanism was proposed.Compressor cascades were simulated using an experimentally validated numerical method to validate the static pressure redistribution mechanism.A geometric parameter named meridional curvature(Cme)is defined to quantify the concave and convex features of the endwall.Results indicate that the contoured endwall changes the streamline curvature,inducing a centrifugal acceleration.Consequently,the radial pressure gradient is reformed to maintain the radial equilibrium.The convex endwall represented by positive Cme increases the radial pressure gradient,decreasing the endwall static pressure,while the concave endwall represented by negative Cme increases the endwall static pressure.The Cme helps to establish the quantified relation between the change in the endwall radial pressure gradient and the endwall geometry.Besides,there is a great correlation between the distributions of the Cme and the change in the endwall static pressure.It can be concluded that the parameter Cme can be considered as a significant parameter to parameterize the endwall surface and to explore the quantitative design strategies of the nonaxisymmetric endwall contouring.

Design and Structural Analysis of Flexible Wearable Chair Using Finite Element Method

The flexible wearable chair is like a light weight mobile exoskeleton that allows people to sit any-where in any working position. The traditional chair is difficult to move to different working locations due to its large size, heavy weight (~5 - 7 kg) and rigid structure and thus, they are inappropriate for workplaces where enough space is not available. Flexible wearable chair has a gross weight of 3 kg as it utilizes light-weight aluminium alloy members. Unlike the traditional chair, it consists of kinematic pairs which enable taking halts between continuous movements at any working position and thus, it is capable of reducing the risk of the physical musculoskeletal disorder substantially among workers. The objective of this paper is to focus on the mechanical design and finite element analysis (FEA) of the mechanism using ANSYS® software. In the present work, all the parts of the mechanism are designed under static load condition. The results of the analysis indicate that flexible wearable chair satisfies equilibrium and stability criterion and is capable of reducing fatigue during working in an assembly line/factory.

AN APPARENT TEMPERATURE MODEL BASED ON THERMAL EQUILIBRIUM

In this paper,a comprehensive analysis and review of the advances in the research of human body comfort degree is made.Based on the studies of human thermal equilibrium theories contributed by previous researchers,different apparent temperature models corresponding to different environments are set up in accordance with the current situation and the characteristics of metabolism in different groups of people in China.After case studies and comparison with present dominant human body comfort degree statistical models,it is proved that the apparent temperature models have high rationality and wide adaptability.Furthermore,the comfort scaling standard according to apparent temperature is suggested,which is suitable for the middle latitude regions in China.