Internal Force Analysis Due to the Supporting Translation in Statically (Indeterminate) Structures for Different Elastic Modulus

For statically indeterminate structure, the internal force will be changed with the translation of the supports, because the internal force is related to the absolute value of the stiffness EI. When the tension is different with the compression modulus, EI is the function of internal force and is not constant any more that is different from classic mechanics. In the other words, it is a nonlinear problem to calculate the internal force. The expression for neutral axis of the statically indeterminate structure was derived in the paper. The iterative program for nonlinear internal force was compiled. One case study was presented to illustrate the difference between the results using the different modulus theory and the single modulus theory as in classical mechanics. Finally, some reasonable suggestions were made for the different modulus structures.

A Two-Stage Method for an Approximate Calculation of Statically Indeterminate Trusses

The paper presents the principles of a method, which in two simple stages makes possible to carry out the statically calculation of values of forces acting in the fiat static indeterminate trusses. In each stage, it is considered the static determinate truss, scheme of which is obtained after remove the suitable number of members from the basic static indeterminate truss. The both intermediate statically determinate trusses are of the same clear span and they are loaded by forces of half values applied to the corresponding truss nodes. The method applies one of the typical procedures of calculation of the statically determinate trusses and then it is applied in an appropriate way the rule of superposition for obtaining the final values of forces acting in particular members of the basic truss. The values of forces calculated in this way are of a very close approximation to the force values determined in the special and complex ways being considered as the exact calculation methods. The proposed method can be useful mostly but not only for the initial structural design of such systems. The simplicity of the two-stage method justifies an assumption that it can be relatively easy and worthy to adjust to the requirements of the computer aided technology of statically calculation of the complex forms of trusses.

A METHOD OF ADJUSTING BAR-LENGTH OF STATICALLY INDETERMINATE TRUSS FOR INCREASING ITS LOAD CAPACITY

Based on the character of the internal force distribution of the statically indeterminate truss, the elements stresses were changed by adjusting the length of bars to increase load capacity of structure. The efficiency of the method is illustrated by several examples.

Examples of Application of Principle of Superposition in the Design of Structural Systems and in Static Analyses

The paper presents general description of combined structural system and initial analysis of an innovative system proposed as the main support structure for tall or heavy loaded buildings located on subsoil of very small load-carrying ability or in earthquake areas. Moreover there is presented also an innovative two-stage method of the approximate calculation of the statically indeterminate trusses. Both are invented by the author by application of the principles of the superposition method.

Analysis of the Results Obtained from the Application of the Two-Stage Method with Calculations of Some Statically Indeterminate Trusses

The paper presents results of calculations of forces in members of selected types of statically indeterminate trusses carriedout by application of the two-stage method of computations of such structural systems. The method makes possible to do the simple andapproximate calculations of the complex trusses in two stages, in each of which is calculated a statically determinate truss being anappropriate counterpart of the basic form of the statically indeterminate truss structure. Systems of the statically determinate trussesconsidered in the both stages are defined by cancelation of members, number of which is equal to the statically indeterminacy of thebasic truss. In the paper are presented outcomes obtained in the two-stage method applied for two different shapes of trusses and carriedout for various ways of removing of appropriate members from the basic trusses. The results are compared with outcomes gained due toapplication of suitable computer software for computation of the same types of trusses and for the same structural conditions.

Three-roller continuous setting round process for longitudinally submerged arc welding pipes

In order to solve the problems of excess ovality and cross-section distortion of longitudinally submerged arc welding pipes after forming,a new three-roller continuous setting round process was proposed.This process can be divided into three stages:loading stage,roll bending stage and unloading stage.Based on the discretization idea,the mechanical model of the primary statically indeterminate problem of the longitudinally submerged arc welding pipes at the roll bending stage was established,and the deformation response was obtained.The simulation and theoretical results show that there are three positive bending regions and three reverse bending regions along the circumference of the pipe.The loading force of each roller shows growth,stability and downward trend with time.The error between the theoretical fitting curve and the simulated data point is very small,and the simulation results verify the reliability of the theoretical calculation.The experimental results show that the residual ovality decreases with the increase of the reduction,and the reduction of the turning point is the optimum reduction.In addition,the residual ovality of the pipe is less than 0.7%without cross-section distortion,which verifies the feasibility of this process.

Closed-Form Modeling and Analysis of an XY Flexure-Based Nano-Manipulator

Flexure-based mechanisms are widely utilized in nano manipulations. The closed-form statics and dynamics modeling is difficult due to the complex topologies, the inevitable compliance of levers, the Hertzian contact interface, etc. This paper presents the closed-form modeling of an XY nano-manipulator consisting of statically indeterminate symmetric(SIS) structures using leaf and circular flexure hinges. Theoretical analysis reveals that the lever’s compliance, the contact stiffness, and the load mass have significant influence on the static and dynamic performances of the system.Experiments are conducted to verify the effectiveness of the established models. If no piezoelectric actuator(PEA) is installed, the influence of the contact stiffness can be eliminated. Experimental results show that the estimation error on the output stiffness and first natural frequency can reach 2% and 1.7%, respectively. If PEAs are installed, the contact stiffness shows up in the models. As no effective method is currently available to measure or estimate the contact stiffness, it is impossible to precisely estimate the performance of the overall system. In this case, the established closed-form models can be utilized to calculate the bounds of the performance. The established closed-form models are widely applicable in the design and optimization of planar flexure-based mechanisms.

Methods for Force Analysis of Overconstrained Parallel Mechanisms： A Review

The force analysis of overconstrained PMs is relatively complex and difficult, for which the methods have always been a research hotspot. However, few liter- atures analyze the characteristics and application scopes of the various methods, which is not convenient for researchers and engineers to master and adopt them prop- erly. A review of the methods for force analysis of both passive and active overconstrained PMs is presented. The existing force analysis methods for these two kinds of overconstrained PMs are classified according to their main ideas. Each category is briefly demonstrated and evaluated from such aspects as the calculation amount, the compre- hensiveness of considering limbs＇ deformation, and the existence of explicit expressions of the solutions, which provides an important reference for researchers and engi- neers to quickly find a suitable method. The similarities and differences between the statically indeterminate prob- lem of passive overconstrained PMs and that of active overconstrained PMs are discussed, and a universal method for these two kinds of overconstrained PMs is pointed out. The existing deficiencies and development directions of the force analysis methods for overconstrained systems are indicated based on the overview.

THE APPLICATIONS OF GENERALIZED VARIATIONAL PRINCIPLES IN NONLINEAR STRUCTURAL ANALYSIS

This paper discusses the generalized variational principles founded by the technique of Lagrangian multipliers in structural mechanics and analyzes the nonlinear statically indeterminate structures. It is assumed that the stress-strain relationship of the materials of structures has the form of namely, the physical equations of structures have the shape of exponential functions. Several examples are given to illustrate the statically indeterminate structures such as the trusses, beams, frames and torsional bars.

Characteristics of Statically Indeterminate Symmetric Flexure Structures

Statically indeterminate symmetric(SIS)flexure structures are symmetric structures with“clamped-clamped”boundary conditions.The static indeterminacy and topological symmetry significantly attenuate the parasitic motions associated with statically determinate flexure structures.Hence,SIS flexure structures feature decoupled linear and angular motions,improved motion accuracy,high stiffness,and high stability.Although SIS flexure structures have been more frequently utilized as prismatic joints,they can also be utilized as revolute joints.This study systematically investigates the characteristics of SIS flexure structures.Based on the unified compliance models of a single flexure hinge,analytical compliance models of two fundamental types of SIS flexure structures are established.In 1-degree-of-freedom or planar applications,multiple SIS-based structures can also be integrated into various configurations to transmit linear or angular motions.Corresponding stiffness models are also established.The characteristics and possible applications of the SIS flexure structures are computationally investigated through case studies.Ultimately,several SIS prototypes are manufactured,and the modeling accuracy of the established stiffness models is experimentally verified.