Preliminary Report on the Theory of Elastic Circular Plate with no Kirchhoff-Love Assumptions

In this paper, the theory of elastic circular plate with no classical Kirchhoff-Love assumptions is established on the basis of a previous paper. In this theory, no classical Kirchhoff-Love assumptions are pre-assumed and the axial symmetrical analytic solution of fixed circular plate under the action of uniform pressure is obtained. Comparison of this solution and the known classical solution shows that this new solution agrees better than classical solution with the experiment measurement.This gives also the quantitative effect of the thickness on the deflection of circular plate with moderate thickness.

THE FIRST-ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORY FOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARYUNDER UNIFORM SURFACE LOADING (Ⅱ)

Based upon Ihe differntial equations and their related boundary conditions givenin the prerious papert[1], this poper finds the analytical solution of non-Kirchhoff-Lovetheory for elastic circular plate with fixed boundary conditions under uniform surfaceloading. However, for the sake of Saving conrputational work. the first orderapproximation theory can be further simplified in more rational bases.

THE FIRST ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORYFOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARY UNDERUNIFORM SURFACE LOADING (Ⅰ)

Based on the approximation theory adopting non-Kirchhoff-Love assumption forthree dimensional elaslic plates with arbitrary shapes[1][2], the author derives afunctional of generalized variation for three dimensional elastic circular plates, therebyobtains a set of differtial equations and the relate boundary conditions to establish afirst order approximation theory for elastic circular plate with fixed boundary andunder uniform loading on one of its surface. The analytical solution of this problemwill present in another paper.

A FURTHER STUDY OF THE THEORY OF ELASTIC CIRCULAR PLATES WITH NON－KIRCHHOFF－LOVE ASSUMPTIONS

Based on the general theory of elastic plates which abandons Kirchhoff-Loveassunption in the classical theory. this paper establishes a first order approximationtheory of elastic circular plates with non-Kirchhoff-Love assumption, and presents ananalytic solution to the axisymmetric problem of elastic circular plates with clampedboundary under uniformly distributed load. By comparing with the classical solution ofthe thin circular plates, it is verified that the new solution is closer to the experimentresults than the classical solution. By virtue of the new theory. the influence of thediameter-to=thickness ratio upon the precision of the classical theory is examined.

APPROXIMATION THEORY OF THREE DIMENSIONAL ELASTIC PLATES AND ITS BOUNDARY CONDITIONS WITHOUT USING KIRCHHOFF－LOVE ASSUMPTIONS

The classical small deflection theory of elastic plates id based on the Kirchhoff-Lore assumptions￣[1,2].Ther are used on the basis of the thinness of plate and the smallness of deflection.In terms of Cartesian tensor coordinates x_i(i=0, 12)these basic assumptions are:(1)the transversal normal strain may be neglected i.e._(00)=0;(2)the transversal shear strain may be neglected i.e.e_(0α)=0(α= 1, 2)(3)the transversal normal stress may be neglected i.e.. σ_(00)=0 .In classical theory of elastic plates,the strain-displacement relations and the corresponding stress-displacement relations are established on the basis of these assumptions. And the equations of the classical theory for a set of undetermined quantities defined on the middle surface are established through integrating the three dimensional equations of equilibrium of stress over the thickness.In the previous papers￣[3,4,5],an approximation theory is given on the basis of Ihree dimensional theory of elastic plates without using Kirchhoff-Love assumptions。However,no uniqueness study is given,and also the boundary conditions have never been studied. In this paper.the same problems are studied on the basis of generalizedvariational principle of the three dimensional theory of elastic bodies￣[6].The stationary conditions of variation give an unique and complete set of field equations and the related boundary conditions for the approximation theory.In this paper,the first order approximation theory is studied in detail.

弹性圆板在一侧受均载而四周固定的条件下不用Kirchhoff-Love假设的一级近似理论(Ⅱ)

本文在前文[1]所得的微分方程和有关边界条件的基础上，求得了这些方程在有关边界条件下的解析解．当然，为了节省计算工作量，我们进一步简化了一级近似理论，使它在保持合理的基础上，更加简单化了．

Finite element modeling assumptions impact on seismic response demands of MRF-buildings

Recent seismic events have raised concerns over the safety and vulnerability of reinforced concrete moment resisting frame ＂RC-MRF＂ buildings. The seismic response of such buildings is greatly dependent on the computational tools used and the inherent assumptions in the modelling process. Thus, it is essential to investigate the sensitivity of the response demands to the corresponding modelling assumption. Many parameters and assumptions are justified to generate effective structural finite element（FE） models of buildings to simulate lateral behaviour and evaluate seismic design demands. As such, the present study focuses on the development of reliable FE models with various levels of refinement. The effects of the FE modelling assumptions on the seismic response demands on the design of buildings are investigated. the predictive ability of a FE model is tied to the accuracy of numerical analysis; a numerical analysis is performed for a series of symmetric buildings in active seismic zones. The results of the seismic response demands are presented in a comparative format to confirm drift and strength limits requirements. A proposed model is formulated based on a simplified modeling approach, where the most refined model is used to calibrate the simplified model.

基本解方法求解简谐外力作用下的Kirchhoff-Love板反源问题

主要考察弹性薄板在规则外力作用下的振动模型.在给定外力源项随时间变化模式的情况下,通过对薄板局部区域一段时间的振动位移观测数据,来反演外力大小的问题,也就是通常所谓的弹性薄板反源问题.给出了弹性薄板反源解的唯一性定理,并推导出板方程的基本解.取基本解方法和Tikhonov正则化方法的精髓,在简谐模式源项作用的情况下,构造了一套算法来反解源项.对Euler-Bernoulli杆和Kirchhoff-Love板的数值算例表明,无论源项是否光滑,测量是否带有误差,基本解方法都因其较好的计算效果,有着广泛的适用性.

Double linear strain distribution assumption of RC beam strengthened with external-bonded or near-surface mounted fiber reinforced plastic

Rehabilitation of existing structures with fiber reinforced plastic(FRP)has been growing in popularity because they offer superior performance in terms of resistance to corrosion and high specific stiffness.The strain coordination results of 34 reinforced concrete beams(four groups)strengthened with different methods were presented including external-bonded or near-surface mounted glass or carbon FRP or helical rib bar in order to study the strain coordination of the strengthening materials and steel rebar of RC beam.Because there is relative slipping between concrete and strengthening materials(SM),the strain of SM and steel rebar of RC beam satisfies the double linear strain distribution assumption,that is,the strain of longitudinal fiber parallel to the neutral axis of plated beam within the scope of effective height(h0)of the cross section is in direct proportion to the distance from the fiber to the neutral axis.The strain of SM and steel rebar satisfies the equation εGCH=βεsteel,where the value of β is equal to 1.1-1.3 according to the test results.

Unsuspected implications arising from assumptions in simulations: insights from recasting a forest growth model in system dynamics

Background:Familiarity with a simulation platform can seduce modellers into accepting untested assumptions for convenience of implementation.These assumptions may have consequences greater than commonly suspected,and it is important that modellers remain mindful of assumptions and remain diligent with sensitivity testing.Methods:Familiarity with a technique can lead to complacency,and alternative approaches and software can reveal untested assumptions.Visual modelling environments based on system dynamics may help to make critical assumptions more evident by offering an accessible visual overview and empowering a focus on representational rather than computational efficiency.This capacity is illustrated using a cohort-based forest growth model developed for mixed species forest.Results:The alternative model implementation revealed that untested assumptions in the original model could have substantial influence on simulated outcomes.Conclusions:An important implication is that modellers should remain conscious of all assumptions,consider alternative implementations that reveal assumptions more clearly,and conduct sensitivity tests to inform decisions.

Analysis of complete plasticity assumption for solid circular shaft under pure torsion and calculation of shear stress

The distribution of shear stress on the cross-section of plastic metal solid circular shaft under pure torsion yielding, the applicability of complete plastic model assumption and the shear stress formula were researched. Based on the shear stress formula of circular shaft under pure torsion in elastic stage, the formula of torque in elastic stage and the definition of yield, it is obtained that the yielding stage of plastic metal shaft under pure torsion is only a surface phenomenon of torque-torsion angle relationship, and the distribution of shear stress is essentially different from that of tensile stress when yielding under uniaxial tension. The pure torsion platform-torsion angle and the shape of torque-torsion angle curve cannot change the distribution of shear stress on the shaft cross-section. The distribution of shear stress is still linear with the maximum shear stress ts. The complete plasticity model assumption is not in accordance with the actual situation of shaft under torsion. The experimental strength data of nine plastic metals are consistent with the calculated results of the new limiting strain energy strength theory （LSEST）. The traditional yield stress formula for plastic shaft under torsion is reasonable. The shear stress formula based on the plane assumption in material mechanics is applicable for all loaded stages of torsion shaft.

Formally Deriving the Third Newton’s Law from a Pair of Nontrivial Assumptions in a Formal Axiomatic Theory “Sigma-V”

The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has continued investigating the extraordinary (paradigm-breaking) hypothesis of formal-axiological interpreting Newton’s mathematical principles of natural philosophy and, thus, has arrived to discrete mathematical modeling a system of formal axiology of nature by extracting and systematical studying its proper algebraic aspect. Along with the proper algebraic machinery, the axiomatic (hypothetic-deductive) method is exploited in this investigation systematically. The research results are the followings. 1) The Third Newton’s Law of mechanics has been modeled by a formal-axiological equation of two-valued algebraic system of metaphysics as formal axiology. (Precise defining the algebraic system is provided.) The formal-axiological equation has been established (and examined) in this algebraic system by accurate computing compositions of relevant evaluation-functions. Precise tabular definitions of the evaluation-functions are given. 2) The wonderful formula representing the Third Newton’s Law (in the relevant physical interpretation of the formal theory Sigma-V) has been derived logically in Sigma-V from the presumption of a-priori-ness of knowledge. A precise axiomatic definition of the nontrivial notion “a-priori-ness of knowledge” is given. The formal derivation is implemented in strict accordance with the rigor standard of D. Hilbert’s formalism;hence, checking the formal derivation submitted in this article is not a difficult task. With respect to proper theoretical physics, the formal inference is a nontrivial scientific novelty which has not been discussed and published elsewhere yet.

AN EFFICIENT BIT COMMITMENT SCHEME BASED ON FACTORING ASSUMPTION

Recently, many bit commitment schemes have been presented. This paper presents a new practical bit commitment scheme based on Schnorr's one-time knowledge proof scheme,where the use of cut-and-choose method and many random exam candidates in the protocols are replaced by a single challenge number. Therefore the proposed bit commitment scheme is more efficient and practical than the previous schemes In addition, the security of the proposed scheme under factoring assumption is proved, thus the cryptographic basis of the proposed scheme is clarified.

TUP: A New eCK-Secure AKE Protocol under the CDH Assumption

The design and analysis of authenticated key exchange protocol is an important problem in information security area. At present, extended Canetti-Krawczyk (eCK) model provides the strongest definition of security for two party key agreement protocol, however most of the current secure protocols can not be prove to secure without Gap assumption. To avoid this phenomenon, by using twinning key technology we propose a new two party key agreement protocol TUP which is obtained by modifying the UP protocol, then in conjunction with the trapdoor test, we prove strictly that the new protocol is secure in eCK model. Compared with previous protocols, the security assumption of new proposal is more standard and weaker, and it also solves an open problem in ProvSec'09.

Assessment of Random Recruitment Assumption in Respondent-Driven Sampling in Egocentric Network Data

One of the key assumptions in respondent-driven sampling (RDS) analysis, called “random selection assumption,” is that respondents randomly recruit their peers from their personal networks. The objective of this study was to verify this assumption in the empirical data of egocentric networks. Methods: We conducted an egocentric network study among young drug users in China, in which RDS was used to recruit this hard-to-reach population. If the random recruitment assumption holds, the RDS-estimated population proportions should be similar to the actual population proportions. Following this logic, we first calculated the population proportions of five visible variables (gender, age, education, marital status, and drug use mode) among the total drug-use alters from which the RDS sample was drawn, and then estimated the RDS-adjusted population proportions and their 95% confidence intervals in the RDS sample. Theoretically, if the random recruitment assumption holds, the 95% confidence intervals estimated in the RDS sample should include the population proportions calculated in the total drug-use alters. Results: The evaluation of the RDS sample indicated its success in reaching the convergence of RDS compositions and including a broad cross-section of the hidden population. Findings demonstrate that the random selection assumption holds for three group traits, but not for two others. Specifically, egos randomly recruited subjects in different age groups, marital status, or drug use modes from their network alters, but not in gender and education levels. Conclusions: This study demonstrates the occurrence of non-random recruitment, indicating that the recruitment of subjects in this RDS study was not completely at random. Future studies are needed to assess the extent to which the population proportion estimates can be biased when the violation of the assumption occurs in some group traits in RDS samples.

Using Excel to Explore the Effects of Assumption Violations on One-Way Analysis of Variance (ANOVA) Statistical Procedures

To understand any statistical tool requires not only an understanding of the relevant computational procedures but also an awareness of the assumptions upon which the procedures are based, and the effects of violations of these assumptions. In our earlier articles (Laverty, Miket, & Kelly [1]) and (Laverty & Kelly, [2] [3]) we used Microsoft Excel to simulate both a Hidden Markov model and heteroskedastic models showing different realizations of these models and the performance of the techniques for identifying the underlying hidden states using simulated data. The advantage of using Excel is that the simulations are regenerated when the spreadsheet is recalculated allowing the user to observe the performance of the statistical technique under different realizations of the data. In this article we will show how to use Excel to generate data from a one-way ANOVA (Analysis of Variance) model and how the statistical methods behave both when the fundamental assumptions of the model hold and when these assumptions are violated. The purpose of this article is to provide tools for individuals to gain an intuitive understanding of these violations using this readily available program.

Homoscedasticity:an overlooked critical assumption for linear regression

SUMMARY Linear regression is widely used in biomedical and psychosocial research.A critical assumption that is often overlooked is homoscedasticity.Unlike normality,the other assumption on data distribution,homoscedasticity is often taken for granted when fitting linear regression models.However,contrary to popular belief,this assumption actually has a bigger impact on validity of linear regression results than normality.In this report,we use Monte Carlo simulation studies to investigate and compare their effects on validity of inference.

Mineralogical and chemical compositions of glauconite and glauconitic rocks and assumption for the formation of the minerals in the Kyzyltokoy basin, Kyrgyzstan

This study is focused on the mineralogical and chemical compositions,deposition environment and mechanism of formation of sediments of Kyzyltokoy basin.By an interpretation of formation,an environment of sedimentation of a basin was separated into three general conditions:a condition where glauconitization process interrupted,where process reached a completion and where occurred decay of glauconites,i.e.,the beginning and interruption in the middle of glauconitization,completion of the

Application and Pullback of the Risk- assumption Principle under Special Circumstances

The risk-assumption principle in infringement is widely used in sport injuries,which is accepted in both the theoretical circle and the juridical practice in China. If the personal injury on the sports ground is not caused by wrongful conducts,the risk-assumption principle is applied,and the doer does not assume compensation liability. If the personal injury is caused by illegality or purposeful illegality to cause personal injury,the risk-assumption principle shall be pulled back totally or partially,and the fault-offset principle and fairly-share-loss principle shall be applied to balance the interests of the two parties. However,under some special circumstances,it is difficult to judge whether there are wrongly conducts; fromthe controversial sports phenomena and sports subjects,this paper analyzes the application and pullback of the risk-assumption principle under some special circumstances.

The Development of Managerial Assumptions about Human Nature in China： A Tale from Quanzhou

How managers’ knowledge and beliefs of human nature are formed and manifested has not been fully explored in the context of Chinese society going through rapid transition nowadays. And yet this could be the missing link in our discourse on Chinese managers. Based on a qualitative study conducted in Quanzhou, China, this study found certain assumptions of human nature that are deeply embedded in their managers’ intellectual framework, which in turn guide their managerial behaviours in diverse aspects of their work. Unless the managers are prepared to examine their own thoughts, especially those at the sub-conscious level, they would remain prisoners of their own thought, and all the efforts directed at transforming managers would be seriously compromised.