Analysis Of Elastic Structures Research Articles

Inelastic Seismic Response of RC Building with Control System

Conventional buildings are mainly designed based on elastic analysis of structures subjected to moderate earthquakes. In this case, the seismic forces are much smaller than the forces introduced by strong ground motions with the considered structural behavior going to nonlinear response during these severe earthquakes. Improving the earthquake resistance of reinforced concrete buildings using a variety of earthquake energy dissipation systems has received considerable attention in recent years by civil engineers. In the present study, a nonlinear computational scheme was developed to predict the complete nonlinear dynamic response of reinforced concrete framed buildings equipped with viscous damper device subjected to earthquake excitation. A finite element program code is developed based on the nonlinear analysis procedure of reinforced concrete buildings equipped with viscous damper devices and a two dimensional, five story models of RC buildings subjected to earthquake were analyzed. Result of nonlinear analysis of RC buildings which furnished by viscous dampers indicated that using of viscous dampers effectively reduced the damages occurring in the building and structural motion during severe earthquakes.

Second-order elastic finite element analysis of steel structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load–displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included. The accuracy and efficiency of the technique is verified by comparisons with a number of plane and spatial structures, whose structural response has been reported in independent studies.

A lumped mass finite element method for vibration analysis of elastic plate-plate structures

The fully discrete lumped mass finite element method is proposed for vibration analysis of elastic plate-plate structures. In the space directions, the longitudinal displacements on plates are discretized by conforming linear elements, and the transverse displacements are discretized by the Morley element. By means of the second order central difference for discretizing the time derivative and the technique of lumped masses, a fully discrete lumped mass finite element method is obtained, and two approaches to choosing the initial functions are also introduced. The error analysis for the method in the energy norm is established, and some numerical examples are included to validate the theoretical analysis.

Creep-fatigue design studies for a sodium-cooled fast reactor with tube sheet-to-shell structure subjected to elevated temperature service

In this paper, creep-fatigue damage under elevated temperatures is investigated for a tube sheet-to-shell structure, which is one of the main structures under Gen-IV class 1 components. To do this, detailed step-by-step procedures, including the elastic structural analysis and the ASME-NH code application, are described for a defined representative load cycle. From the sensitivity studies for various design parameters, such as hold time duration, shell thickness, and operating temperature, it is found that a reduction of thickness can decrease the thermal bending stresses, but the negative effect is that it may increase the primary stress and enhance the creep damage. The normal operating temperature is the most significant parameter in the creep-fatigue design.

Mechanical and geometric advantages in compliant mechanism optimization

This paper presents a focused examination of the mechanical and geometric advantages in compliant mechanisms and their ramifications in the design formulations of compliant mechanisms posed as a topology optimization problem. With a linear elastic structural analysis, we quantify mechanical (and geometric) advantage in terms of the stiffness elements of the mechanism’s structure. We then analyze the common formulations of compliant mechanism optimization and the role of the external springs added in the formulations. It is shown that the common formulations using mechanical (or geometric) advantage would directly emulate at best a rigid-body linkage to the true optimum design. As a result, the topology optimization generates point flexures in the resulting optimal mechanisms. A case study is investigated to demonstrate the resulting trends in the current formulations.

Static analysis of two-dimensional elastic structures using global collocation

Based on previous findings concerning the numerical solution of one-dimensional elastodynamical problems [Provatidis in Arch Appl Mech 78(4):241–250, 2008] this paper extends the methodology to the static analysis of two-dimensional problems in quadrilateral domains. This target is achieved by replacing the Galerkin/Ritz procedure involved in Lagrangian (or Gordon–Coons) type finite elements by a global collocation scheme. In brief, the boundary conditions are fulfilled at all boundary nodes, while the governing equation is fulfilled at internal points. The theory is supported by four test cases concerning rectangular and curvilinear structures under plane-stress or plane-strain conditions, where the convergence rate is successfully compared with that of conventional bilinear finite elements with the same mesh density.

Shakedown and collapse of elastic-plastic structures under variable and cyclic loads

The paper presents an introduction to the results obtained mainly by the author in shakedown analysis of elastic plastic structures, with the shakedown theorems for elastic plastic kinematic hardening materials playing the central role. Some illustrative examples of application are given.

A finite element method for vibration analysis of elastic plate-plate structures

The semi and fully discrete finite element methods are proposed for investigating vibration analysis of elastic plate-plate structures. In the space directions, the longitudinal displacements on plates are discretized by conforming linear elements, and the corresponding transverse displacements are discretized by the Morley element, leading to a semi-discrete finite element method for the problem under consideration. Applying the second order central difference to discretize the time derivative, a fully discrete scheme is obtained, and two approaches for choosing the initial functions are also introduced. The error analysis in the energy norm for the semi and fully discrete methods are established, and some numerical examples are included to validate the theoretical analysis.

Free vibration multiquadric boundary elements applied to plane elasticity

This paper presents a new boundary element formulation for free vibration analysis of two-dimensional elastic structures. The dual reciprocity method (DRM) is introduced using the multiquadric radial basis functions (MQ). The required particular solution kernels for displacement and traction are derived and smoothed using simple mathematical trick; hence the limiting values of these kernels are computed. The eigen-problem of displacement is formulated and solved to obtain the required frequencies of different vibration modes. Finally, several numerical problems are studied to demonstrate the validity and accuracy of the developed formulation. The results are compared to those obtained from other interpolation functions, and finite element analysis to demonstrate the validity and superiority of the present formulation.

Vibration analysis for elastic multi‐beam structures by the C0‐continuous time‐stepping finite element method

AbstractSome C0‐continuous time‐stepping finite element method is proposed for investigating vibration analysis of elastic multi‐beam structures. In the time direction, the C0‐continuous Galerkin method is used to discretize the generalized displacement field. In the space directions, the longitudinal displacements and rotational angles on beams are discretized using conforming linear elements, while the transverse displacements on beams are discretized by the Hermite elements of third order. The error of the method in the energy norm is proved to be O(h+k3), where h and k denote the mesh sizes of the subdivisions in the space and time directions, respectively. The finite difference analysis in time is developed to discuss the spectral behavior of the algorithms as well as their dissipation and dispersion properties in the low‐frequency regime. The method has also been extended to study some nonlinear problems. A number of numerical tests are included to illustrate the computational performance of the method. Copyright © 2008 John Wiley & Sons, Ltd.

On use of the Dirac delta function in the vibration analysis of elastic structures

The Dirac delta function has often been employed to represent the amplitude of concentrated harmonic forces in the analysis of vibration of elastic structures such as beams and plates. It is known that this function, as represented by a truncated Fourier series, does not provide a true representation of a concentrated force, nevertheless, it is frequently employed and good convergence is usually, though not always, encountered in solutions thereby obtained. In this paper, the nature of the function is discussed and for illustrative purposes it is used to obtain series solutions for some selected beam and plate free vibration problems. In some cases problems are chosen for which exact solutions are already obtainable by analytical means. This permits powerful checks to be made on rates of convergence experienced when the series solutions are investigated. Rates of convergence are discussed in detail and it is explained why convergence is to be expected when analyzing certain families of problems when employing this function and a lack of convergence is to be expected in others.

Parametric analyses on the initial stiffness of flush end-plate splice connections using FEM

Existing design procedures for steel frames have been modified during the last three decades to incorporate the semi-rigid behavior of the connections into the frame design advancement. Knowledge in initial rotational stiffness of a connection is important for the global elastic analysis of frame structures. This paper presents the results of several parametric analyses on the Initial Rotational Stiffness (IRS or S ini ) of Bolted Flush End-plate Beam (BFEB) splice connections using Finite Element Modeling (FEM). The FEMs have taken into account material behavior, geometrical discontinuities and large displacements. The analyses have been calibrated to experimental results that are also briefly reviewed in this paper. These models clearly support the numerical results and show accurate correlation between FEM and experimental results of the connections behavior. Due to the multitude of influencing parameters, an analytical description of the BFEB connections behavior has been delivered. This is based on component method, which is proposed by the Eurocode 3 as the equivalent T-stub. Also comparisons between numerical and analytical data for initial slop of moment–rotation curves are accomplished. The method for accuracy in predicting values regarding the S ini of BFEB connection is also discussed.

A smoothed four-node piezoelectric element for analysis of two-dimensional smart structures

This paper reports a study of linear elastic analysis of two-dimensional piezoelectric structures using a smoothed four-node piezoelectric element. The element is built by incorporating the strain smoothing method of mesh-free conforming nodal integration into the standard four-node quadrilateral piezoelectric finite element. The approximations of mechanical strains and electric potential fields are normalized using a constant smoothing function. This allows the field gradients to be directly computed from shape functions. No mapping or coordinate transformation is necessary so that the element can be used in arbitrary shapes. Through several examples, the simplicity, efficiency and reliability of the element are demonstrated. Numerical results and comparative studies with other existing solutions in the literature suggest that the present element is robust, computationally inexpensive and easy to implement.

Linear elastic isoparametric spline finite strip analysis of perforated thin-walled structures

This paper describes the application of the isoparametric spline finite strip method to the linear elastic analysis of tri-dimensional perforated folded plate structures. The general theory of the isoparametric spline finite strip method is introduced. Kinematics assumptions and the procedure for combining in-plane (membrane) and bending effects are set out. Particular attention is paid to the procedure for rotating the stiffness matrix and load vector from local to global coordinates. The reliability of the method is demonstrated by comparisons with finely meshed finite element analysis results. Square stiffened perforated plates in compression and bending are analysed.

Elastic buckling analysis of perforated thin-walled structures by the isoparametric spline finite strip method

This paper presents the application of the isoparametric spline finite strip method to the elastic buckling analysis of perforated folded-plate structures. The general theory of the isoparametric spline finite strip method is introduced. The kinematics assumptions, strain–displacement and constitutive relations of the Mindlin plate theory are described and applied to the spline finite strip method. The corresponding matrix formulation is utilised in the equilibrium and stability equations to derive the stiffness and stability matrices. A number of numerical examples of flat and folded perforated plate structures illustrate the applicability and accuracy of the proposed method.

The Boundary Element Method and Path-independent Integrals in Sensitivity Analysis of Structures with Stress Concentration

This paper presents the implementation of the boundary element method to shape sensitivity analysis of elastic structures with stress concentrators. An elastic body which contains a number of voids (internal boundaries), playing the role of stress concentrators, is considered. We are interested in calculating the first order sensitivity of shape–dependent functionals with respect to the shape variation of the body domain. This task is accomplished using the adjoint variable method. As it has been shown by Dems and Mróz [10], for a basic transformation (i.e. a translation, a rotation or a scale change) of the body, the sensitivity of the considered functional takes the form of a path-independent integral (PII) whose integrand depends on the primary and adjoint state fields, along an arbitrary path (curve in 2D, surface in 3D), enclosing the transformed stress concentrator (void). It is very important for numerical computations, because we can compute this integral along the path placed far from the stress concentrator to eliminate the negative influence of stress concentrations on the accuracy of calculations. The boundary element method (BEM) is used to solve both primary and adjoint problems. Some important cases of adjoint problems related to functionals are analyzed in the paper. A thorough numerical verification of the proposed method is performed in this work. The presented method of sensitivity analysis is utilised in gradient-based optimization and identification problems. Numerical examples of optimization and identification are shown in this paper.

Probabilistic analysis of linear elastic cracked structures

This paper presents a probabilistic methodology for linear fracture mechanics analysis of cracked structures. The main focus is on probabilistic aspect related to the nature of crack in material. The methodology involves finite element analysis; statistical models for uncertainty in material properties, crack size, fracture toughness and loads; and standard reliability methods for evaluating probabilistic characteristics of linear elastic fracture parameter. The uncertainty in the crack size can have a significant effect on the probability of failure, particularly when the crack size has a large coefficient of variation. Numerical example is presented to show that probabilistic methodology based on Monte Carlo simulation provides accurate estimates of failure probability for use in linear elastic fracture mechanics.

Modelisation of thermoelastic linear behaviour of tungsten filaments in simple and twin helical spring configurations

By trying to increase the luminosity or the life expectancy of an incandescent lamp, an idea consists of a series of successive rolling up of the tungsten filament. This gives geometrical configurations of filaments named simple, twin, or triple helical spring, etc… In this paper, we will limit only to the cases of the simple and twin helical spring filaments. Under the combined effects of the high temperature and the stresses induced by its own weight, the filament creeps by becoming plastically deformed in a permanent and a continuously manner, until the rupture. The theoretical study of the behaviour of these filaments needs the knowledge of internal efforts distribution, deformations modes, and their evolutions. The present work consists on an elastic structural analysis which must be the first step. Since the objective is also to study the influence of the filament self-weight solicitation, the orientation (or position) with respect to gravitational direction should be taken into account. Numerical results are obtained by finite element method. They showed a negligible influence of the solicitations due to the variation of the temperature with respect to those of the self-weight, and a relative sensitivity to the position changes for the twin helical spring filament. For this later, we have developed an analytical method which is only valid in the case of a vertical position. Because of some difficulties, the comparison between the numerical and analytical results could not be carried out directly. However, the analytical approach proved to be qualitatively useful for the analysis of numerical results.

Explicit a posteriori error estimates for eigenvalue analysis of heterogeneous elastic structures

An a posteriori error estimator is developed for the eigenvalue analysis of heterogeneous elastic structures. It constitutes an extension of a well-known explicit estimator to heterogeneous structures. We prove that our estimates are independent of the variations in material properties and independent of the polynomial degree of finite elements. Finally, we study numerically the effectivity of this estimator on several model problems.

The dual reciprocity method applied to free vibrations of 2D structures using compact supported radial basis functions

This paper presents a new boundary element application for free vibration analysis of 2D elastic structures. The dual reciprocity method is applied using four compact supported radial basis functions for approximating the domain inertia terms. The eigen-problem of displacement is then solved considering the traction contribution by means of static condensation. The formulation is also extended to consider additional internal nodes to improve accuracy. Three numerical problems are studied to demonstrate the validity and accuracy of the developed formulation. The results are compared to those obtained from analytical and other numerical solutions. A parametric study is set up to demonstrate the effect of the compact support radius on the final results and on the sparsity of system matrices.