Method Of Initial Parameters Research Articles

Distortional analysis of simply supported box girders with inner diaphragms considering shear deformation of diaphragms using initial parameter method

In this paper, the distortion of simply supported girders with inner diaphragms subjected to concentrated eccentric loads is investigated using initial parameter method (IPM), in which the in-plane shear deformation of diaphragms is fully considered. A statically indeterminate structure was modeled with inner redundant forces, where the interactions between the girder and diaphragms were indicated by a distortional moment. Considering the compatibility condition between the girder and diaphragms, solutions for the distortional angle, warping displacements and stresses were derived and further simplified by establishing a matrix equation system. The validity of IPM was intensively verified by a finite element analysis and distortional experiments. Parametric studies were then performed to examine the effect of the diaphragm number on the distortional angle, warping displacements and stresses under various ratios of height to span of the girder and the diaphragm thicknesses. Besides, stabilities of the local web plate and mid-span diaphragm were analyzed based on IPM for box girders with symmetrical three inner diaphragms. Results show that the local web plate will buckle before overall yielding with the increment of the eccentric loads Pj, and the mid-span diaphragm is constantly stable in the whole deformation process. It shows that more attentions should be paid on the stability of the local web plate than overall yielding for girders subjected to eccentric loads.

Analysis of the distortion of cantilever box girder with inner flexible diaphragms using initial parameter method

In this paper, the distortion of cantilever box girders with inner flexible thin diaphragms is investigated under concentrated eccentric loads using initial parameter method (IPM), in which the in-plane shear strain of diaphragms is fully considered. A high-order statically indeterminate structure was established with redundant forces, where the interactions between the girder and diaphragms were indicated by a uniform distortional moment. Based on the compatibility condition between the girder and diaphragms, solutions for the distortional angle and the warping function were obtained by using IPM. The accuracy of IPM was verified by finite element analysis for the distortion of cantilever box girders with 2, 5 and 9 diaphragms under three diaphragm thicknesses, respectively. Taking a lifting mechanism as an example, parametric studies were then performed to examine the effects of the diaphragm number and thickness, the ratio of height to span of the girder, the hook's location and the wheels' positions on the distortion of cantilever box girders. Numerical results were summarized into a series of curves indicating the distribution of distortional warping stresses and displacements for various cross sections and loading cases.

A revised solution for the horizontal vibration of an end‐bearing pile in viscoelastic soil

AbstractThis note presents a new method to derive closed‐form expressions describing the horizontal response of an end‐bearing pile in viscoelastic soil subjected to harmonic loads at its head. The soil surrounding the pile is assumed as a linearly viscoelastic layer. The propagation of waves in the soil and pile is treated mathematically by three‐dimensional and one‐dimensional theories, respectively. Unlike previous studies of the problem, the formulation presented allows the governing equations of the soil to be solved directly, eliminating the need to introduce potential functions. Accordingly, the dynamic response of the pile is obtained by means of the initial parameter method, invoking the requirement for continuity at the pile–soil interface. It is demonstrated that the derived compact solution matches exactly an existing solution that utilises potential functions to formulate the problem. Copyright © 2016 John Wiley & Sons, Ltd.

Free vibration analysis of axially functionally graded beams using method of initial parameters in differential form

Free vibration analysis of axially functionally graded beams using method of initial parameters in differential form

Numerical method for stability analysis of functionally graded beams on elastic foundation

This paper considers the problems of stability of non-uniform and axially functionally graded (FG) Euler–Bernoulli beams on elastic foundation. The boundary conditions of the beam are given in general form covering different classical supporting conditions. Furthermore, the boundary conditions are transformed into convenient form in order to avoid handling infinity values of the stiffness coefficients. The method of initial parameters in differential form is used for the numerical solution of the problem. The solution of the posed boundary value problem is reduced to the iterative solution of two initial value problems and homogeneous linear algebraic system of order two. The Richardson extrapolation method is employed to improve the accuracy of results. The performance of the method proposed has been validated by several numerical examples.

Analysis of the Process of Turning of Low-Rigidity Shafts

A machining station, working together with a lathe, was designed and constructed for the stabilisation of the axis of low-rigidity parts in the process of machining. The basic element is a self-centring lunette with hydraulic drive, allowing part centring without any preliminary alignment. The methodology of calculation of the parameters of the “semi-finished product/supports” subsystem is given. The effect of various schematics of support arrangements on the dynamics of the semi-finished product was analysed. The analysis of schemes of low-rigidity part fixing in the device for the stabilisation of its axis was conducted with the method of initial parameters. The choice of supports and the positioning of backstays and/or buffering steady rests was also analysed for increasing the stationary character of the process of machining and the quality of shaping the machined surface.

Torsional behaviour of curved composite beams in construction stage and diaphragm effects

During the concrete-casting process of curved steel–concrete composite beams in construction stage, all loads including the wet concrete weight are carried by the curved open thin-walled steel girder. In order to determine the required diaphragm spacing, firstly the curved girder is simplified to straight one by using the M/r method, and its torsional behaviour is subsequently derived by solving the restrained torsional differential equation with the initial parameter method, where the discrete diaphragms are treated to be equivalent to a continuous elastic thin plate. Taking the maximum stress ratio of the warping normal stress to the bending normal stress as the control index, effects of the number of diaphragms, the span of the curved girder, the span-to-radius ratio, the girder height and the flange width on the stress ratio are studied. The parametric analysis results indicate that with the increase of the number of diaphragms, the stress ratio decreases exponentially; and with the increase of the span-to-radius ratio, the warping stress ratio increases linearly; additionally, longer span leads to reduced stress ratios, but the variation of the girder height and the flange width has little influence on the stress ratio. Calculation formulae for determining the required diaphragm spacing are obtained eventually by regression analyses. Based on the research outcomes herein, given the limit value of the warping stress ratio in the practical design of curved composite beams under construction, the maximum diaphragm spacing of the open thin-walled steel girder can be determined by using the formulae proposed in this paper.

中部任意位置定向支承加固的压杆稳定性计算

为了丰富压杆的稳定性研究内容和方便工程应用之目的，用初参数法，对中部任意位置增加一个定向支承加固的七种压杆，建立了统一的变形方程和静力平衡方程。由各自的变形和静力约束条件，导出了求解临界压力的特征方程。借助软件，求得了压杆的长度因数与中部支承位置间的近似或精确关系；同时确定了中部支承的最佳位置和最小长度因数，以及最差位置和最大长度因数。经验证，结果符合理论预期。 For enriching the research content about the stability of a long column and making it convenient in the engineering application, by using the initial parameters method, seven kinds of long column are strengthened by directional support in any position of central, and the unified deformation equa-tions and static force equilibrium equations are established. By the respective constraint conditions of deformation and static force, the characteristic equations of critical force are solved. By software, the approximate or accurate relationship between the factor of length of long column and the posi-tion of the central directional support are determined; at the same time, the best position of the central directional support and the minimum factor of length, and the worst position and the maximum factor of length are all determined. The result is verified according with theoretical expectation.

Simplified Dynamic Analysis of Grinders Spindle Node

Abstract The contribution deals with the simplified dynamic analysis of surface grinding machine spindle node. Dynamic analysis is based on the use of the transfer matrix method, which is essentially a matrix form of method of initial parameters. The advantage of the described method, despite the seemingly complex mathematical apparatus, is primarily, that it does not require for solve the problem of costly commercial software using finite element method. All calculations can be made for example in MS Excel, which is advantageous especially in the initial stages of constructing of spindle node for the rapid assessment of the suitability its design. After detailing the entire structure of spindle node is then also necessary to perform the refined dynamic analysis in the environment of FEM, which it requires the necessary skills and experience and it is therefore economically difficult. This work was developed within grant project KEGA No. 023TUKE-4/2012 Creation of a comprehensive educational - teaching material for the article Production technique using a combination of traditional and modern information technology and e-learning.

New approach for the vibrations of inhomogeneous orthotropic cylindrical shells resting on step-wise Winkler foundations

In this paper, Flügge’s shell theory and solution for the vibration analysis of an inhomogeneous, orthotropic cylindrical shell resting on a circumferentially stepped Winkler foundation are carried out. The stepwise foundation consists of two regions having different stiffnesses and both regions are symmetric about the centrelines of the shell. The governing equations of the shell are formulated as a three-dimensional boundary-value problem and their solutions are obtained by a numerical–analytical approach. The trigonometric functions are used with Fourier’s approach to approximate the solution in the longitudinal direction and also to reduce the two-dimensional problem to one-dimensional one. Using the transfer matrix approach and based on the method of initial parameters, these equations can be written in a matrix differential equation of first order in the circumferential coordinate and solved numerically as an initial-value problem. The proposed model is applied to get the inverse vibration frequencies and the corresponding mode shapes of the shell vibrations. The sensitivity of the vibration behaviour and bending deformations to the geometry of Winkler foundation, homogeneity variation and shell orthotropy is investigated for different type-modes of vibration.

Horizontal impedance of pile groups considering shear behavior of multilayered soils

The impedances and internal force distributions of a pile and pile groups subjected to horizontal harmonic pile-head loads have been studied. A layered Pasternak model, which overcomes the limitation of the Winkler model, that ignores the shear stiffness of the soil, is developed to describe the reaction of the soil on piles. The differential equation of the horizontal damped vibrations of a pile is solved by the initial parameter method, combined with transfer-matrix formulations, to deal with the layered property of the soil. The superposition approach, based on the interaction factors, is taken to estimate the effects of pile groups. The precision and the applicability of the method are demonstrated through this study. Comparing the results of the Pasternak model and the Winkler model, it is revealed that the role of soil shear has an influence on the impedances of a single pile and pile groups, especially in the case of a low pile–soil modulus ratio.

Effect of a forced harmonic vibration pile to its adjacent pile in layered elastic soil with double-shear model

A new model named double-shear model based on Pasternak foundation and Timoshenko beam theory is developed to evaluate the effect of a forced harmonic vibration pile to its adjacent pile in multilayered soil medium. The double-shear model takes into account the shear deformation and the rotational inertia of piles as well as the shear deformation of soil. The piles are simulated as Timoshenko beams, which are embedded in a layered Pasternak foundation. The differential equation of transverse vibration for a pile is solved by the initial parameter method. The dynamic interaction factors for the layered soil medium are obtained by the transfer matrix method. The formulation and the implementation have been verified by means of several examples. The individual shear effects of soil and piles on the interaction factors are evaluated through a parametric study. Compared to Winkler model with Euler beam, the present model gives much better results for the dynamic interaction of piles embedded in stiff soil with small slenderness ratios. Finally, the effect of a forced long pile to a short pile embedded in multilayered soil medium is studied in detail.

Simplified Calculation of the Eccentric Press Stiffness

The article deals with the simplified calculation of the stiffness of the eccentric press frame. The described method applies to the solving of problem a mathematical identification of condition parameters in the press frame the transfer matrix method (TMM), which is in essence a matrix form of initial parameters method. This method is suitable for mechanical systems with continuously distributed mass in space while the cross-sections along the entire length of the system are not constant.

Restrained Torsion of Thin-Walled Beams

AbstractA first-order torsion formulation for closed thin-walled (CTW) beam subjected to restrained torsion is developed to consider the warping deformation and restrained shear stresses on cross section and their effect on the behavior of thin-walled (TW) beam. The total torque on closed cross section in the current formulation consists of four component torques. The expressions of various torques and corresponding shear stresses are given. To account for the distribution of true restrained shear stress due to restrained shear rotation in TW cross section, torsion shear coefficient is proposed for CTW beam. Like the transverse shear coefficient in Timoshenko beam theory, the torsion shear coefficient lies at the heart of the first-order torsion theory. The new governing equations of restrained torsion of CTW beam are obtained, which have obvious physical meaning and is easy to be used in engineering and can also be used to solve the torsion problem of open thin-walled beam. The initial parameter method i...

STUDY ON TUBE SHELL TRANSVERSE DISPLACEMENTS UNDER ITS MACHINING BASED ON COMPUTER SIMULATION

The possibility to increase parameter accuracy (pitch of thread, pressure angle, external and internal thread diam eter) for various kinds of thread on the seamless casing is studied. As a means of achieving the targ et goal, the v ibration amplitude contraction arising in the system ‘machine — widget — tool — part’ is considered (MWTP). To solve the problem, a model which describes tube shell oscillations in the course of its processing a nd allows defining the impact on the work end of shell oscillations arising in its loose part is offered. The study is resulted in a math ematical model b ased on the initial parameters method. The calculations found the best (of the considered in the paper) support location diagram under which the arising oscillations are the lowest. The obtained re sults can be used at any enterprise dealing with thread cut ting on the casing tubes. The investigation results in the following: — optimum quantity of supports for the considered equipment is five; — expansion in the number of supports by no means always leads to the vibration amplitude contraction; — changing in the relative position of supports is an effective means of the vi bration amplitude contraction that acts to increa se thread parameters accuracy.

Thermally Induced Piezothermoelastic Fields of a Smart Sandwich Cylindrical Structure with a Functionally Graded Interlayer

An effective approach is developed to analyze the piezothermoelastic behavior of a smart sandwich cylindrical structure which is made of a functionally graded (FG) elastic interlayer and two pyroelectric layers at its surfaces. The pyroelectric layers are homogeneous and the material properties of the elastic interlayer are assumed to be the functions of radius. Laminate model is employed to approximate the FG interlayer. The temperature field is obtained by means of the initial parameter method. The solutions of the elastic and electric fields in the FG elastic interlayer are developed by means of the state space method and the Cayley-Hamilton principle. Numerical results show that the material's nonhomogeneity and the stacking sequence play important roles on the piezothermoelastic behavior of a smart sandwich cylindrical structure when it is served in thermal environment.

Original Computer Based Solutions in Structural Studies

The paper is inspired by the computer based solutions developed over a period of almost 30 years. Thus, the original computer based solutions were developed for a wide range of problems: computer aided geometry for domain definition, data generators for finite element applications, output data file processors with visualization facilities, matrices defined as random access files with a wide range of subsequent applications in several disciplines and domains of science, FDM and FEM applications, customized solutions for heat transfer problems, computational fluid dynamics, experimental data reduction software applications, virtual reality facilities, semi-numeric modeling, computer based decisions. Dedicated solutions were developed for applied elasticity problems related to marine engineering problems as we as naval architecture problems: ship strength computing based on the method of initial parameters, geometrical characteristics of the cross sections, automatic calculus of the stresses of a general-shaped section and others. Most of these applications present the output data in a graphical way, in order to be more relevant for a structural analyst. Another objective was to offer not only values of different parameters, but laws of variation which may be used in other subsequent analytic studies. According to the complexity of the problem to be solved, these applications are in a range which starts at the data-crunching level up to complex and intelligent solutions, some of them being implemented in programs of tens of thousands of computer code lines. The paper presents the main features of each computer based solution, the connectivity with other solutions, the possibility to extend or adapt a given solution for a particular case study. Last but not least, there must be noticed that computer based solutions may be used in several directions of development: research, design and education..

An effective approach for transient thermal analysis in a functionally graded hollow cylinder

An effective approach is developed to analyze the transient thermal analysis in a functionally graded hollow cylinder. The heat conductivity, mass density and specific heat are assumed to vary along the radial direction with arbitrary grading pattern. The transient solution in the radial direction is obtained based on the laminate approximation theory. In solving technique, the transient solution is divided into two parts: One is quasi-static solution and the other is dynamic solution. The quasi-static solution is obtained by the state space method and the dynamic solution is obtained by the initial parameter method. In this analysis, all the manipulation is performed in time domain. In the illustrative examples, the effect of the inhomogeneity form on the transient thermal responses is investigated.

Analysis of pile subjected to torsion in multi‐layered soil

SummaryA new method of analysis of piles in multi‐layered elastic soil subjected to a torque at the head is developed. The differential equation governing the angle of twist in the pile is derived using the variational principles of mechanics. The method of initial parameters is used to obtain closed‐form solutions of the angle of twist and torque in the pile as a function of depth. The inputs required for the analysis are shear moduli of pile and soil, pile geometry and thickness of soil layers. Copyright © 2013 John Wiley & Sons, Ltd.

Analytical solution of two-dimensional transient heat conduction in fiber-reinforced cylindrical composites

An analytical solution is obtained for two-dimensional transient heat conduction in a fiber-reinforced multilayer cylindrical composites. Separation of variables method is employed to develop the transient temperature fields. In the polar coordinates, the presented analytical solution contains trigonometric series and Bessel series. Both the sine series and the cosine series are included in the trigonometric series. To deal with the continuity conditions at the interfaces, the initial parameter method is used and the solution is derived only by operating two by two matrices. The solving procedure is performed directly in time domain and the Laplace transform is avoided. The effect of the fibers' angle on the transient heat conduction behaviors is investigated.