Analysis Of Elastic Structures Research Articles

Natural element approximation of Reissner–Mindlin plate for locking-free numerical analysis of plate-like thin elastic structures

A rotation-free mixed natural element approximation of Reissner–Mindlin plate for the locking-free numerical analysis of plate-like thin elastic structures is presented, motivated by the rotation-free approximation for plate- and shell-like elastic structures and the high smoothness of Laplace interpolation functions used in natural element method. The mid-surface deflection and the rotation of shear are directly approximated using Laplace interpolation functions, while the Voronoi polygon-wise constant curvatures and bending moments are indirectly computed by area-averaging the boundary integrals of deflection derivatives and rotation of shear. The present approximation of the deflection and rotation of shear of discretized Reissner–Mindlin plate bending problem is formulated according to the modified mixed Hu-Washizu principle. Through the numerical results, it is verified that the rotation-free mixed natural element approximation of only the deflection and rotation of shear successfully prevents shear locking in the numerical analysis of plate-like thin elastic structures.

Comparisons of High-Temperature Structural Analysis Results on the Medium-Scale PHE Prototype under the Steady-State and Trip Conditions of a Small-Scale Gas Loop

PHE (Process Heat Exchanger) is a key component for transferring the high-temperature heat generated from a VHTR (Very High Temperature Reactor) to a chemical reaction for massive production of hydrogen. Recently, Korea Atomic Energy Research Institute (KAERI) has manufactured a medium-scale PHE prototype made of Hastelloy-X of high-temperature alloy and a performance test on the PHE prototype is scheduled in a small-scale nitrogen gas loop established at KAERI. In this study, in order to evaluate the high-temperature structural integrity of the PHE prototype under the steady-state and trip conditions of the gas loop before the performance test on the PHE prototype, elastic and elastic-plastic structural analyses on the PHE prototype were carried out and the analyses results were compared each other.

A novel versatile multilayer hybrid stress solid-shell element

This paper presents a versatile multilayer locking free hybrid stress solid-shell element that can be readily employed for a wide range of geometrically linear elastic structural analyses, i.e. from shell-like isotropic structures to multilayer anisotropic composites. This solid-shell element has eight nodes with only displacement degrees of freedom and a few internal parameters that provide the locking free behavior and accurate interlaminar stress resolution through the element thickness. These elements can be stacked on top of each other to model multilayer structures, fulfilling the interlaminar stress continuity at the interlayer surfaces and zero traction conditions on the top and bottom surfaces of composite laminates. The element formulation is based on the modified form of the well-known Fraeijs de Veubeke---Hu---Washizu (FHW) multifield variational principle with enhanced assumed strains (EAS formulation) and assumed natural strains (ANS formulation) to alleviate the different types of locking phenomena in solid-shell elements. The distinct feature of the present formulation is its ability to accurately calculate the interlaminar stress field in multilayer structures, which is achieved by incorporating an assumed stress field in a standard EAS formulation based on the FHW principle. To assess the present formulation's accuracy, a variety of popular numerical benchmark examples related to element patch tests, convergence, mesh distortion, shell and laminated composite analyses are investigated and the results are compared with those available in the literature. This assessment reveals that the proposed solid-shell formulation provides very accurate results for a wide range of structural analyses.

An optimal versatile partial hybrid stress solid-shell element for the analysis of multilayer composites

SUMMARY In the present contribution we propose an optimal low-order versatile partial hybrid stress solid-shell element that can be readily employed for a wide range of geometrically linear elastic structural analyses, that is, from shell-like isotropic structures to multilayer anisotropic composites. This solid-shell element has eight nodes with only displacement degrees of freedom and only a few internal parameters that provide the locking-free behavior and accurate interlaminar shear stress resolution through the element thickness. These elements can be stacked on top of each other to model multilayer composite structures, fulfilling the interlaminar shear stress continuity at the interlayer surfaces and zero traction conditions on the top and bottom surfaces of composite laminates. The element formulation is based on the modified form of the well-known Fraeijs de Veubeke–Hu–Washizu multifield variational principle with enhanced assumed strains formulation and assumed natural strains formulation to alleviate the different types of locking phenomena in solid-shell elements. The distinct feature of the present formulation is its ability to accurately calculate the interlaminar shear stress field in multilayer structures, which is achieved by the introduction of the assumed interlaminar shear stress field in a standard enhanced assumed strains formulation based on the Fraeijs de Veubeke–Hu–Washizu principle. The numerical testing of the present formulation, employing a variety of popular numerical benchmark examples related to element patch test, convergence, mesh distortion, shell and laminated composite analyses, proves its accuracy for a wide range of structural analyses.Copyright © 2012 John Wiley & Sons, Ltd.

Seismic performance of eccentrically braced frame with vertical link using PBPD method

SUMMARYThere are special guidelines to design the structures resistant to earthquake forces; parameters such as conditions of the site, seismicity of the site, importance of the structure and the type of the structure are the main effective factors. Consideration of these parameters in calculation and distribution of the earthquake forces are significantly different in various design codes. In most of these design codes, the computation and distribution of earthquake forces are based upon the elastic structural analysis. In this approach, the real behavior of structure is not considered and it may consequently sustain big displacements and irretrievable damages. Therefore, a new design method has been utilized in this paper by which the base shear and its distribution in the height of the structure are calculated according to the plastic behavior of structure and takes advantage of energy balance. The latter is known as performance‐based plastic design method. The study of the behavior of eccentrically braced frames with vertical links while undertaking earthquake loads using performance‐based plastic design method is the main purpose of this study. It is also worthy of notion that the frames are designed using a capacity design method. In addition, the results are compared with those of the International Building Code 2009 method; the results demonstrate that the plastic hinges, the interstory drifts and plastic rotation of links are distributed more uniformly in the height of frames designed by the suggested method compared to International Building Code 2009. Copyright © 2012 John Wiley & Sons, Ltd.

Effect of Weld Properties on the Thermo-Mechanical Structural Analysis of Prototype Process Heat Exchanger

A PHE (Process Heat Exchanger) is a key component in transferring the high temperature heat generated from a VHTR (Very High Temperature Reactor) to the chemical reaction for the massive production of hydrogen. A performance test on a small-scale PHE prototype made of Hastelloy-X is currently under way a small-scale gas loop at the Korea Atomic Energy Research Institute. Previous research on the elastic high-temperature structural analysis of the small-scale PHE prototype has been performed using the parent material properties over the whole region. In this study, an elastic-plastic high-temperature structural analysis considering the mechanical properties in the weld-affected zone was performed, from a macroscopic viewpoint.

Three Dimensional Vibration Analysis of a Class of Traction-Free Solid Elastic Bodies with an Eccentric Cavity

A three-dimensional elasticity-based continuum model is developed for describing the free vibrational characteristics of an important class of isotropic, homogeneous, and completely free structural bodies (i.e., finite cylinders, solid spheres, and rectangular parallelepipeds) containing an arbitrarily located simple inhomogeneity in form of a spherical or cylindrical defect. The solution method uses Ritz minimization procedure with triplicate series of orthogonal Chebyshev polynomials as the trial functions to approximate the displacement components in the associated elastic domains, and eventually arrive at the governing eigenvalue equations. An extensive review of the literature spanning over the past three decades is also given herein regarding the free vibration analysis of elastic structures using Ritz approach. Accuracy of the implemented approach is established through proper convergence studies, while the validity of results is demonstrated with the aid of a commercial FEM software, and whenever possible, by comparison with other published data. Numerical results are provided and discussed for the first few clusters of eigen-frequencies corresponding to various mode categories in a wide range of cavity eccentricities. Also, the corresponding 3D mode shapes are graphically illustrated for selected eccentricities. The numerical results disclose the vital influence of inner cavity eccentricity on the vibrational characteristics of the voided elastic structures. In particular, the activation of degenerate frequency splitting and incidence of internal/external mode crossings are confirmed and discussed. Most of the results reported herein are believed to be new to the existing literature and may serve as benchmark data for future developments in computational techniques.

Three dimensional vibration analysis of a class of traction-free solid elastic bodies with an eccentric cavity

A three-dimensional elasticity-based continuum model is developed for describing the free vibrational characteristics of an important class of isotropic, homogeneous, and completely free structural bodies (i.e., finite cylinders, solid spheres, and rectangular parallelepipeds) containing an arbitrarily located simple inhomogeneity in form of a spherical or cylindrical defect. The solution method uses Ritz minimization procedure with triplicate series of orthogonal Chebyshev polynomials as the trial functions to approximate the displacement components in the associated elastic domains, and eventually arrive at the governing eigenvalue equations. An extensive review of the literature spanning over the past three decades is also given herein regarding the free vibration analysis of elastic structures using Ritz approach. Accuracy of the implemented approach is established through proper convergence studies, while the validity of results is demonstrated with the aid of a commercial FEM software, and whenever possible, by comparison with other published data. Numerical results are provided and discussed for the first few clusters of eigen-frequencies corresponding to various mode categories in a wide range of cavity eccentricities. Also, the corresponding 3D mode shapes are graphically illustrated for selected eccentricities. The numerical results disclose the vital influence of inner cavity eccentricity on the vibrational characteristics of the voided elastic structures. In particular, the activation of degenerate frequency splitting and incidence of internal/external mode crossings are confirmed and discussed. Most of the results reported herein are believed to be new to the existing literature and may serve as benchmark data for future developments in computational techniques.

Two Scale Analysis of Elastic Structures of Particle Reinforced Composite Materials with Finite Element Method

Particle reinforcement method is an important measure to improve the properties of materials.To predict the relationships among micro structures and mechanical properties of a composite material is a basis to realize stronger of materials.It is favorable to introduce multi-scale models in order to investigate the influence of micro structures on macro mechanical properties for better analysis,design and optimation of composite materials.Based on homogenization theory,using Voronoi cell finite element method to perform numerical simulation to particle reinforced composite materials.The macro equivalent elastic constants of a composite material can be predicted,and the micro stress fields are attained directly.In micro scale,the equilibrated stress fields are first assumed,and Voronoi stress cells are adopted to get the complimentary energy functional,so that the control equations can be established,and a set of linear algebraic equations that can be directly resolved is formed.Finally,the stress coefficients are calculated and the micro stress fields are attained.In macro scale,the macro structure analysis is done with the finite element analysis software ANSYS.The macro average value of elastic module is calculated by homogenization method,which is inputed into the ANSYS system to perform calculations.So that the two scales of macro and micro can be coupled and a mechanical analysis can be executed to the structures made of particle reinforced composite materials.

Improved Algorithm for Efficient and Realistic Creep Analysis of Large Creep-Sensitive Concrete Structures

Recent compilation of data on numerous large-span prestressed segmentally erected box girder bridges revealed gross underestimation of their multi-decade deflections. The main cause has been identified as incorrect and obsolete creep prediction models in various existing standard recommendations and is being addressed in a separate study. However, previous analyses of the excessive deflections of the Koror-Babeldaob (KB) Bridge in Palau and of four Japanese bridges have shown that a more accurate method of multi-decade creep analysis is required. The objective of this paper is to provide a systematic and comprehensive presentation, appropriate not only for bridges but also for any large creep-sensitive structure. For each time step, the solution is reduced to an elastic structural analysis with generally orthotropic elastic moduli and eigenstrains. This analysis should normally be three-dimensional (3-D). It can be accomplished with a commercial finite element code such as ABAQUS. Based on the Kelvin chain model, the integral-type creep law is converted to a rate-type form with internal variables, which account for the previous history. For time steps short enough to render aging during each step to be negligible, a unique continuous retardation spectrum for each step is obtained by Laplace transform inversion using simple Widder's formula. Discretization of the spectrum then yields the current Kelvin chain moduli. The rate-type creep analysis is computationally more efficient than the classical integral-type analysis. More importantly, though, it makes it possible to take into account the evolution of various inelastic and nonlinear phenomena such as tensile cracking, cyclic creep, and stress relaxation in prestressing tendons at variable strain, as well as the effects of humidity and temperature variations, and the effect of wall thickness variation on drying creep and shrinkage. Finally, the advantages compared to the existing commercial programs, based on step-by-step integration of memory integrals, are pointed out and illustrated by a simple example.

Evaluation of Representative Loading Frequency for Linear Elastic Analysis of Asphalt Pavements

The mechanistic design of flexible pavement is usually done with linear elastic theory (LET); this process must use appropriate values of the equivalent asphalt concrete elastic modulus to evaluate stresses and strains in a linear elastic multilayer. The aim is to identify some relationships to estimate the value of loading frequency, representative of the real strain pulse frequency spectrum, to be used in calculating the stiffness modulus of the asphalt concrete layers. In this way, an equivalent linear elastic structural analysis can be conducted. To achieve this aim, many transient load simulations were performed with ViscoRoute software based on the viscoelastic model. After variables that affected the representative frequency value were detected, more than 215 variable combinations (representative of real conditions) were randomly generated. For each combination, viscoelastic analysis was conducted, and then the stiffness modulus and the corresponding loading frequency were backcalculated by minimizing the residuals between linear elastic and viscoelastic peak strains. The representative frequency values calculated for these configurations were related to the significant variables by means of a multivariate regression. The model was developed separately for each of the three directions according to the anisotropic behavior of pavement under moving loads. Finally, the procedure was validated by applying it to several climatic and load configurations of an existing pavement. A simple and useful tool is provided to take into account all significant parameters; the tool can be used in conjunction with LET for pavement design.

Elastic stability analysis of cold-formed pallet rack structures with semi-rigid connections

This paper describe the three dimensional finite element modeling and elastic buckling analysis of single 2-D and 3-D frame (with semi-rigid connection) of conventional pallet racking system. Results from experimental study, effective length approach given by Rack Manufacturer's Institute (RMI) and finite element analysis of single 2-D frames of cold-formed steel pallet racking are compared. Finite element model used for single 2-D frame is further extended for 3-D frames with semi- rigid connection and results of these 3-D frames are also presented in the paper. Finite element analysis carried out on conventional pallet racks using the finite element program ANSYS with the 18 types of developed column sections. The principal aims were to find out the linear buckling load of single 2-D frames and to ascertain stability of 3-D frames of conventional pallet racking systems, made up of cold-formed sections with semi-rigid connection. Investigation into stability analysis of frames used in pallet rack structures by both experimental and finite element methods have shown that stiffening of the open upright sections using the spacer bar, channel and hat as external stiffeners will considerably increase the load carrying capacity of the frames.

Refined shell model for the linear analysis of isotropic and composite elastic structures

A refined finite element shell model has been developed in this work using an eight-nodes element with nine degrees of freedom for each node. This model enhances the classical shell approaches by including the transverse normal strain. The three displacement components are quadratically expanded in the thickness direction, therefore the transverse shear and normal strains effects are included in such a model making it suitable for thin and thick multilayered composite structures. The transverse normal strain is linear in the thickness direction z and the related shell theory is free from Poisson locking. Finite element locking mechanisms (shear and membrane locking) have been opportunely corrected: good convergence rate has been shown for the considered shell problems (with various geometries, thickness ratios and stacking layer sequences). No shear correction factors are requested.

Geometric and material nonlinear analysis of tensegrity structures

A numerical method is presented for the large deflection in elastic analysis of tensegrity structures including both geometric and material nonlinearities. The geometric nonlinearity is considered based on both total Lagrangian and updated Lagrangian formulations, while the material nonlinearity is treated through elastoplastic stress-strain relationship. The nonlinear equilibrium equations are solved using an incremental-iterative scheme in conjunction with the modified Newton-Raphson method. A computer program is developed to predict the mechanical responses of tensegrity systems under tensile, compressive and flexural loadings. Numerical results obtained are compared with those reported in the literature to demonstrate the accuracy and efficiency of the proposed program. The flexural behavior of the double layer quadruplex tensegrity grid is sufficiently good for lightweight large-span structural applications. On the other hand, its bending strength capacity is not sensitive to the self-stress level.

Elastic sectional stress analysis of variable section piers subjected to three-dimensional loads

The elastic stress analysis of beam-column structures of uniaxial symmetrical variable cross-sections is developed using an extension of Euler–Bernoulli beam theory. The applied loads are general considering axial (P), flexure (Mx–My), shear (Vx–Vy), and torsion (T). Three-dimensional analytical solutions for normal and shear stresses are derived using sectional analysis with warping functions for variable boundaries in elevation. The differential equations of equilibrium and deformations are accounting for the variations in the geometrical properties of the cross-section and related boundary conditions. The strong form solution is then written in a weak form that is implemented in a 2D sectional finite element (FE) code assuming linear normal stress distribution. Three application examples are presented to validate the proposed sectional approach and illustrate its accuracy by comparing with results from full 3D FE analyses: (a) a slender rectangular section pier with a sloped boundary, (b) a bulk rectangular section buttress with unsymmetrical slopes, and (c) a pier (squat wall) for a hydraulic structure. When the assumption of linear distribution for normal flexural stress is satisfied, the proposed sectional approach produces results within 1% of 3D FE with much reduced computational efforts. For bulk and squat walls the stress field distribution are very similar to 3D FE while the stress intensity shows some variations. This is of major practical significance because the proposed approach allows performing first a series of simplified yet acceptable sectional analyses in safety assessment of the three-dimensional type of structures considered herein.

A mixed solid-shell element for the analysis of laminated composites

SUMMARY This paper presents a versatile low order locking-free mixed solid-shell element that can be readily employed for a wide range of linear elastic structural analyses, that is, from thick isotropic structures to multilayer anisotropic composites. This solid-shell element has eight nodes with only displacement degrees of freedom and few assumed stress parameters that provide very accurate interlaminar stress calculations through the element thickness. These elements can be stacked on top of each other to model multilayer structures, fulfilling the interlaminar stress continuity at the interlayer surfaces and zero traction conditions on the top and bottom surfaces of the laminate. The element formulation is based on the well-known Fraeijs de Veubeke–Hu–Washizu mixed variational principle with enhanced assumed strains formulation and assumed natural strains formulation to alleviate the different types of locking phenomena in solid-shell elements. The distinct feature of the present formulation is its ability to accurately calculate the interlaminar stress field in multilayer structures, which is achieved by the introduction of a constraint equation on the interlaminar stresses in the Fraeijs de Veubeke–Hu–Washizu principle-based enhanced assumed strains formulation. The intelligent computer coding of the present formulation makes the present element appropriate for a wide range of structural analyses. To assess the present formulation's accuracy, a variety of popular numerical benchmark examples related to element convergence, mesh distortion, and shell and laminated composite analyses are investigated and the results are compared with those available in the literature. These benchmark examples reveal that the proposed formulation provides very good results for the structural analysis of shells and multilayer composites. Copyright © 2011 John Wiley & Sons, Ltd.

Reliability analysis of uncertain structures using earthquake response spectra

This paper develops a probabilistic methodology for the seismic reliability analysis of structures with random properties. The earthquake loading is assumed to be described in terms of response spectra. The proposed methodology takes advantage of the response spectra and thus does not require explicit dynamic analysis of the actual structure. Uncertainties in the structural properties (e.g. member cross-sections, modulus of elasticity, member strengths, mass and damping) as well as in the seismic load (due to uncertainty associated with the earthquake load specification) are considered. The structural reliability is estimated by determining the failure probability or the reliability index associated with a performance function that defines safe and unsafe domains. The structural failure is estimated using a performance function that evaluates whether the maximum displacement has been exceeded. Numerical illustrations of reliability analysis of elastic and elastic-plastic single-story frame structures are presented first. The extension of the proposed method to elastic multi-degree-of-freedom uncertain structures is also studied and a solved example is provided.

Stress Buildup of Sn3.5Ag Soldered Stacked CSPs to Board-Level Drop Impact

Solder balls, albeit mechanically soft, are the only structural support to the stacking of chip-scale packages (CSPs). This paper investigates the structural response of a Sn3.5Ag soldered bi-level stacked CSP module to board-level drop impact per the JEDEC criteria, and quantifies the stress buildup in the critical solder balls. The structural response is understood by tracking the force transmission through this 3-D packaging assembly by an elastic structural analysis, in which the solder plasticity is deliberately excluded. The elastic analysis shows that the solder balls at the ball-out level, which is the bottom level of the stacked package interconnecting to the mounting board, suffer the severest stress buildup. The results suggest that understanding of relative vibration amplitude among each level of the stacked package and the mounting board enables a good estimation of the location of critical solders without detailed modeling. For this stacked CSP module, the critical solders locate at the corners of the center package at the ball-out level. Solder balls are more severely loaded in the 0° orientation drop, about one order of magnitude larger than in the 90° orientation drop. The critical solder balls will be promptly loaded to a state in the highly plastic regime after the impact is initiated, as suggested by detailed finite element analysis which accounts for the strain-hardening of Sn3.5Ag. Larger plastic strain accumulation is observed near the interfaces to the solder pad. The solder balls at the higher level of the stacked packages are likely always free of plastic deformation in the drop testing.

On the interdependency of primary and initial secondary equilibrium paths in sensitivity analysis of elastic structures

The scientific motivation for this paper is lack of clarity about the interdependency of primary and initial secondary equilibrium paths in the frame of sensitivity analysis of elastic structures. The investigation of this interdependency comprises of the following four cases: (1) nonlinear primary path, nonlinear stability problem, (2) linear primary path, nonlinear stability problem, (3) nonlinear primary path, linear stability problem, and (4) linear primary path, linear stability problem. The consistently linearized eigenproblem is used for differentiation of two classes of nonlinear stability problems with markedly different characteristics of both the prebuckling and the postbuckling behavior. For one of them, e.g. zero-stiffness postbuckling is impossible. For the other one, which is restricted to a prebuckling regime with axial deformations only, sensitivity analysis of the initial postbuckling behavior either exhibits its continuous improvement or its continuous deterioration, depending on whether the bifurcation point diverges from or converges to the snap-through point. In other words, a monotonic variation of the design parameter cannot result in a non-monotonic change of the initial postbuckling behavior. The practical motivation for this work is to explore the mechanical reasons for qualitatively different modes of transition from imperfection sensitivity to insensitivity in the course of sensitivity analysis for the purpose of improving the postbuckling behavior of structures by means of minor design changes. Results from a numerical investigation corroborate the theoretical findings.

ADVANCED MODEL REDUCTION METHOD FOR ELASTIC EARTHQUAKE RESPONSE ANALYSIS OF SHEAR BUILDINGS WITH SETBACK

An advanced reduced model is proposed for elastic earthquake response analysis of shear building structures with setback. The proposed reduction method consists of two parts. The first stage is the construction of a reduced structural model with the degrees of freedom at representative floor levels only. The reduced model is constructed using an inverse eigenmode-problem formulation so as to have the same fundamental natural frequency and lowest-mode component ratios at the representative floor levels as the original model. The second stage is the transformation of earthquake input forces into a set of reduced input forces. This transformation is introduced to enhance the accuracy level of the reduced model.