Hybrid Stress Research Articles

Hybrid Stress Testing by Adenosine Infusion and Exercise Myocardial Perfusion Imaging: A Critical Appraisal

Hybrid Stress Testing by Adenosine Infusion and Exercise Myocardial Perfusion Imaging: A Critical Appraisal

Hybrid Stress Testing by Adenosine Infusion and Exercise Myocardial Perfusion Imaging: A Critical Appraisal

Hybrid Stress Testing by Adenosine Infusion and Exercise Myocardial Perfusion Imaging: A Critical Appraisal

An assumed-stress hybrid element for static and free vibration analysis of folded plates

A four-node hybrid stress element for analysing orthotropic folded plate structures is presented. The formulation is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. The proposed element has six degree of freedom per node and permits an easy connection to other type of elements. An equilibrated stress field in each element and inter element compatible boundary displacement field are assumed independently. Static and free vibration analyses of folded plates are carried out on numerical examples to show that the validity and efficiency of the present element.

Accurate 4‐node quadrilateral elements with a new version of energy‐compatible stress mode

AbstractA 4‐node hybrid stress quadrilateral element is presented with compatible isoparametric bilinear displacements and a new version of 5‐parameter stresses which satisfies both self‐equilibrium equations and an energy orthogonal relation between stress terms and Wilson incompatible strains. Based on different element formulations, another two new elements are also derived and shown to be identical to the first element. Numerical benchmark experiments show that the three equivalent elements possess high accuracy at coarse meshes, are frame invariant and free from Poisson locking at the nearly incompressible limit. Since the 5‐parameter stress mode used does not have uncoupled constant terms, the elements do not pass the patch test. Copyright © 2006 John Wiley & Sons, Ltd.

Plane hybrid stress elements for 3D analysis of moderately thick solids subjected to loading symmetric to midsurface

Plane semi-analytical hybrid stress elements are formulated from the 3D Hellinger–Reissner principle for modelling moderately thick structural components with and without hollows subjected to loadings symmetric to the midsurface. These components possess symmetry in the thickness direction but could not be idealised as either plane stress or plane strain problems. 3D displacement and stress fields conforming to the exact plane stress solution are assumed and normal stresses on the surfaces parallel to the thickness direction are nullified. These 2D elements possess good convergence characteristics and simulate the 3D behaviour of solids whose stress free surfaces exhibit negligible out-of-plane distortion with good level of accuracy comparable to 3D analyses by ABAQUS.

Experimental investigation of cyclic and time-dependent deformation of titanium alloy at elevated temperature

A novel cyclic deformation test program was undertaken to characterize macroscopic time dependent deformation of a titanium alloy for use in viscoplastic model development. All tests were conducted at a high homologous temperature, 650 °C, where there are large time dependent and loading rate dependent effects. Uninterrupted constant amplitude tests having zero mean stress or a tensile mean stress were conducted using three different control modes: strain amplitude and strain rate, stress amplitude and stress rate, and a hybrid stress amplitude and strain rate. Strain ratcheting occurred for all cyclic tests having a tensile mean stress and no plastic shakedown was observed. The shape of the strain ratcheting curve as a function of time is analogous to a creep curve having primary, steady state and tertiary regions, but the magnitude of the ratchet strains are higher than creep strains would be for a constant stress equal to the mean stress. Strain cycles interrupted with up to eight 2-h stress relaxation periods around the hysteresis loop, including hold times in each quadrant of the stress–strain diagram, were also conducted. Stress relaxation was path-dependent and in some cases the stress relaxed to zero. The cyclic behavior of these interrupted tests was similar even though each cycle was very complex. These results support constitutive model development by providing exploratory, characterization and validation data.

A simple hybrid stress element for shear deformable plates

AbstractA new quadrilateral 4‐node element for shear deformable plates is developed based on the hybrid stress formulation. The element is designed to be simple, stable, free of locking and to pass all the patch tests. To this purpose, special attention is devoted to select displacement and stress approximations. The standard displacement interpolation is enhanced by linking the transverse displacement to the nodal rotations and an appropriate stress approximation is rationally derived. In particular, the assumed stress approximation is equilibrated within each element, co‐ordinate invariant and ruled by the minimum number of parameters. Excellent element performance is demonstrated by a wide experimental evaluation. Copyright © 2005 John Wiley & Sons, Ltd.

An Electric Node Concept for Solid-Shell Elements for Laminate Composite Piezoelectric Structures

The eight-node solid-shell finite element models have been developed for the analysis of laminated composite plate/shell structures embedded with piezoelectric actuators and sensors. To resolve the locking problems of the solid-shell elements in laminated materials and improve accuracy, the assumed natural strain method and hybrid stress method are employed. Introduction of the concept of the electric nodes can effectively eliminate the burden of constraining the equality of the electric potential for the nodes lying on the same electrode. Furthermore, the nonlinear electric potential distribution in piezoelectric layer is described by introducing internal electric potential. The developed finite element models, especially electric potential node model, are simpler over other models but can still obtain same accuracy as exact solution described. Several examples are studied and compared with exact solution and other predicted results to illustrate the accuracy of the present model, and efficacy and effect caused by nonlinear electric potential distribution on frequency and electric fields in smart structure modeling.

The hybrid boundary element method in structural acoustics

AbstractThis paper presents a new symmetric formulation for structural acoustics in the frequency domain. Usually, the structural domain is discretized with the Finite‐Element Method (FEM), whereas the Boundary Element Method (BEM) is used for the treatment of the infinite acoustic domain. Coupling formulations generally suffer from the dense and unsymmetric equation system of the BEM. To circumvent this drawback, the acoustic domain is discretized here with the Hybrid Stress Boundary Element Method (HSBEM), which is based on a variational principle. The discretized formulation consists of a symmetric stiffness‐type equation based on a dynamic flexibility matrix in frequency domain. The HSBEM is thus easily coupled with other symmetric discretization methods, combining the advantages of a boundary formulation and a symmetric approach. An issue of the method is the evaluation of the flexibility matrix. This contribution extends former publications of the authors by a detailed analysis of the implementation of this matrix, leading to a new clustering scheme for an efficient treatment, based on the special structure of the integral kernel. Moreover, the treatment of hyper‐singular integral kernels without integration, based on orthogonality properties for interior and exterior domains is outlined. Examples show the consistency of this approach. Finally, a coupled formulation for structural acoustics employing the HSBEM for the structure and the acoustic domain is introduced. Several numerical tests elucidate the applicability of the method and the proposed improvements.

Boundary Element Methods for Engineers and Scientists: An Introductory Course With Advanced Topics

11R1. Boundary Element Methods for Engineers and Scientists: An Introductory Course With Advanced Topics. - L Gaul, M Ko¨gl, and M Wagner. Springer-Verlag, New York. 2003. 488 pp. ISBN 3-540-00463-7. $79.95. Reviewed by JT Chen (Dept of Harbor and River Eng, Natl Taiwan Ocean Univ, PO Box 7-59, Keelung 202, Taiwan, ROC).As the title of this book emphasizes, an introductory course to the boundary element method (BEM) and advanced formulations is presented. The book contains four parts: Part I The Direct Boundary Element Method, Part II Dual Reciprocity Method (DRM), Part III Hybrid Boundary Element Methods, and Part IV Appendix. Part I can be seen as an introductory course, while Parts II and III cover advanced topics that contain the authors’ research material. The appendices in Part VI contain some fundamental solutions and particular solutions for the DRM. Exercises and programs are not provided. The reviewer found that an on-line book of BEM by the first author is available on the web site of http://www.bem.uni-stuttgart.de/. This site provides a more friendly and suitable textbook for beginners since exercises are given. As it is common with other BEM books, this text begins with an introduction and mathematically preliminaries. A special chapter on continuum physics is added in Chapter 3: the basic laws and constitutive equations for elastodynamics, heat conduction, electrodynamics, thermoelasticity, acoustics, and piezoelectricity are covered to provide a complete overview on the physical modeling. Chapters 4 and 5 introduce the direct BEM for potential problems of the Laplace and Navier equations with emphases on the issues of anisotropy and piezoelectricity. No indirect formulations in terms of single-layer or double-layer representations are developed. Numerical integration schemes for regular and singular integrals are addressed in Chapter 6. Parts II and III on advanced topics include the dual reciprocity BEM and the hybrid BEM. Chapter 7 basically follows the DRM book by Partridge et al. for a general introduction to the method. Chapter 8 focus on the solution of the DRM equation of motion and Chapters 9 and 10 present the application of the DRM to piezoelectricity and thermoelasticity. The hybrid BEM is derived from variational principles of mechanics that are reviewed in Chapter 11. Hybrid displacement and hybrid stress methods are both addressed in Chapters 12 and 13, respectively. Since the presented hybrid BEM uses the same source of variational principles as for hybrid FEM, one obtains symmetric system matrices. In contrast to symmetric Galerkin BEM, the hybrid BEM does not require a double integration over the boundary. Although this book can be used as a text in a BEM course, it contains some original results regarding the dual reciprocity BEM and the variational formulation of the hybrid BEM. The book is thus recommended to graduate students and engineers. The authors have succeeded in fulfilling their aim of a dual-purpose textbook. In Part I, students as well as practitioners find a clear introduction to the method, whereas Parts II and III can serve as a valuable reference to researchers and engineers. The main distinction of the book in comparison to available works on the BEM may be its focus on the application of the method to anisotropy, piezoelectricity and thermoelasticity, as well as the presentation of the hybrid BEM. The book contains 488 pages with 135 figures. The quality of print and figures is adequate. In general, this is a well-written book and is recommended to individuals and libraries.

An accurate hybrid macro-element with linear displacements

A hybrid stress quadrilateral macro-element HQM is proposed. Compatible linear displacements are used on its two triangular sub-domains, and a 5-parameter incomplete linear stress mode is suggested. Equivalence to another quadrilateral element HQ4 with compatible isoparametric bilinear displacements is proven. Due to elimination of stress parameters at the element level, the computational cost of HQM/HQ4 is as same as that of Q4. Numerical tests show that the element is accurate, insensitive to mesh distortions, and free from Poisson locking. Copyright © 2004 John Wiley & Sons, Ltd.

Straight free-edge effects in laminated composites

A new three-dimensional hybrid stress element with a traction-free planar surface has been developed for efficient analysis of the interlaminar stresses near traction-free straight boundaries. All 3D stress components are included and are interpolated independently within each layer. The expressions of six stress components are derived, such that the homogeneous equilibrium equations in each layer, the continuity of transverse stresses on the interlayer surface, the traction-free boundary conditions over the planar surface and lower surface of the laminated composite are satisfied a priori, while the interelement reciprocity condition is satisfied a posteriori through a Lagrange multiplier method. The use of such special element in the finite element solution has been shown to be highly accurate when only a very coarse element mesh is used near the free-edge.

Accurate solution of traction free boundaries using hybrid stress membrane elements with drilling degrees of freedom

Methodologies for the accurate solution of traction free sides using hybrid stress membrane elements with drilling degrees of freedom are presented. Firstly, a method based on direct enforcement of the traction free condition through manipulation of the elemental assumed stress field is presented. Secondly, a penalty-equilibrated approach, in which stress equilibrium is enforced in individual elements, is presented. In the second approach, weak enforcement of equilibrium is proposed, in which the stress derivatives are modified as to alleviate locking-like behavior.

Non-conventional non-linear two-node hybrid stress-strain curved beam elements

This paper presents a family of two-node hybrid stress–strain curved beam elements with four displacement degrees of freedom (dof) per node for the finite deformation 2D Timoshenko beam theory, which can be readily generalized on the two-node curved beam elements with six displacement dof for the 3D beam theory. The developed formulation is based on the principally new non-linear strain–displacement relationships that are objective, i.e., invariant under arbitrarily large rigid-body motions. To avoid shear and membrane locking and have no spurious zero energy modes, the assumed stress resultant and strain fields are invoked. In order to circumvent thickness locking, the modified material stiffness matrices corresponding to the plane stress state are employed. The fundamental unknowns consist of four displacements and five strains of the face lines of the beam, and five stress resultants. The element characteristic arrays are obtained by using the Hu-Washizu variational principle. To demonstrate the efficiency and accuracy of this formulation and to compare its performance with other non-linear finite element models reported in the literature, extensive numerical studies are presented.

Interlaminar Stress and Delamination Analysis of Internally-Tapered Composite Laminates

In the present work, the interlaminar fracture behavior of internally-tapered composite laminates that have cracks in the drop-off region is investigated using J-integral and direct calculation methods. The influences of cracks at the resin layer–interleaf interface and at the interface between adjacent plies are studied. The composite laminate is modeled and analyzed using partial hybrid stress finite elements that are formulated based on the Hellinger–Reissner variational principle and the generalized plane deformation theory. In the formulation, only three interlaminar stress components that cause delamination at the interface are independently assumed in addition to displacement interpolation. Both the six-node triangular and eight-node quadrilateral hybrid finite elements (formulated and presented in a companion paper [He, K., Hoa, S.V. and Ganesan, R. “Stress Analysis of Tapered Composite Laminate Using Partial Hybrid Finite Elements”, J. Reinforced Plastics and Composities, 23:6, 2004.]) are used in the fracture analysis. A parametric study is conducted to determine the influences of geometric and material properties on the fracture behavior of the tapered laminate. Experimental work was carried out for the observation of fracture. The analysis results and the experimental observation are compared.

ハイブリッド型応力法Timoshenkoはり柱要素について : (その2) 複合はり柱要素の構築とその応用

ハイブリッド型応力法Timoshenkoはり柱要素について : (その2) 複合はり柱要素の構築とその応用

Non-conventional non-linear two-node hybrid stress-strain curved beam elements

This paper presents a family of two-node hybrid stress–strain curved beam elements with four displacement degrees of freedom (dof) per node for the finite deformation 2D Timoshenko beam theory, which can be readily generalized on the two-node curved beam elements with six displacement dof for the 3D beam theory. The developed formulation is based on the principally new non-linear strain–displacement relationships that are objective, i.e., invariant under arbitrarily large rigid-body motions. To avoid shear and membrane locking and have no spurious zero energy modes, the assumed stress resultant and strain fields are invoked. In order to circumvent thickness locking, the modified material stiffness matrices corresponding to the plane stress state are employed. The fundamental unknowns consist of four displacements and five strains of the face lines of the beam, and five stress resultants. The element characteristic arrays are obtained by using the Hu-Washizu variational principle. To demonstrate the efficiency and accuracy of this formulation and to compare its performance with other non-linear finite element models reported in the literature, extensive numerical studies are presented.

FEM formulation of four and five noded elements using a linearly varying stress assumption

The two-dimensional stress analysis is investigated to develop multi-noded elements that can be used in a finite element mesh. To accomplish this, a hybrid stress element is developed assuming a linear stress variation within the element. The formulation for this type of element is developed for a multi-noded polygon consisting of up to five nodes however simplifies to a constant stress element for a triangle. The formulation differs from the method developed by Pian [AIAA J. 2 (1964) 1333]. In the formulation discussed in this article, the same matrix is used to relate stress to constant stress parameters, and strain to constant strain parameters. This approximation simplifies the formulation, however does not significantly impact the results. The effectiveness of the formulation and code implementation is illustrated through “patch tests” along with other examples to assess this approximation. The linear stress element developed in this article is shown to be robust, yielding reasonable results even when a poorly designed finite element mesh is used in the cantilever beam example. In addition, the article includes a comparison between the linear stress element and the constant strain element to illustrate the advantages of the linear stress element over the constant strain element approach.

Optimization of stress modes by energy compatibility for 4‐node hybrid quadrilaterals

AbstractOptimal hybrid stress quadrilaterals can be obtained by adopting appropriate stresses and displacements, and satisfying the energy compatibility condition is shown to be an ultimate key to obtaining optimal stress modes. By using compatible isoparametric bilinear (Q4) displacements and 5‐parameter energy compatible stresses of the combined hybrid finite element CH(0‐1), a robust 4‐node plane stress element ECQ4 is derived. Equivalence to another hybrid stress element LQ6 with 9‐parameter complete linear stresses based on a modified Hellinger–Reissner principle is established. A convergence analysis is given and numerical experiments show that elements ECQ4/LQ6 have high performance, i.e. are accurate at coarse meshes, insensitive to mesh distortions and free from locking. Copyright © 2003 John Wiley & Sons, Ltd.

A 4-noded hybrid stress element with optimized stress for moderately thick and thin shallow shells

In this paper, a 4-noded hybrid stress finite element is developed for arbitrary plates and shallow shells. The finite element formulation is derived from the Hellinger–Reissner functional. In the process of the element derivation, the optimization principle of the numerical behaviour of multiple-variable FEM, in which an energy compatible condition is introduced to optimise the unconstrained stress trials, is employed. An appropriate unconstrained stress field is carefully chosen to validate the optimization. Because the transverse shear effect is taken into account, the element can be used for moderately thick and thin plates and shallow shells. Numerical study demonstrates that the present element passes the patch test and is of high accuracy and free of superfluous zero energy deformation modes. There is no shear locking in the limit of thin plates and shells.