Spatial stability of shear deformable curved beams with non-symmetric thin-walled sections. I: Stability formulation and closed-form solutions

For spatial stability analysis of shear deformable thin-walled curved beams with non-symmetric cross-sections, an improved analytical formulation is proposed. Firstly the displacement field is introduced considering the second order terms of semi-tangential rotations. Next an elastic strain energy is derived by using transformation equations of displacement parameters and stress resultants and considering shear deformation effects due to shear forces and restrained warping torsion. And then the potential energy due to initial stress resultants is consistently derived with accurate calculation of Wagner effect. In addition, closed-form solutions for in-plane and lateral-torsional buckling loads of curved beams subjected to uniform compression and pure bending are newly derived. In the companion paper, FE procedures are developed by using curved and straight beam elements with arbitrary thin-walled sections. In numerical examples, to illustrate accuracy and validity of this study, closed-form solutions for in-plane and out-of-plane buckling loads are presented and compared with those obtained from analytical solutions by other researchers.     

Post-buckling behavior of thin steel plates using computational models

Thin plates loaded in plane will buckle at very small loads, and due to unavoidable out-of-plane imperfections, the theoretical buckling load cannot be observed experimentally. If the plate is adequately supported along its boundaries, it will be able to carry a much higher load than the theoretical buckling load.Computational models can be used to study the post buckling behaviour of thin plate structures up to failure. Failure of such structures is usually due to large out-of-plane deflections, yielding, and rupture. Therefore, the computational model should include the effects of geometric and material nonlinearities. In this paper, the nonlinear finite element analysis program NONSAP and ANSR-III were modified and used in the analysis. Since these programs did not include the suitable elements and material properties to conduct the subject study, new elements and new material properties were added to the programs. In particular, a thin shell element was added and the solution routines were modified to improve its accuracy and efficiency.The modified programs were used on a Super Computer to calculate the post buckling strength of stiffened and unstiffened plates subjected to uniaxial compression, and plates subjected to in plane bending or shear. Crippling of plates subjected to in-plane or eccentric edge compressive loads was also examined. The results from the computational models were compared with test results and reasonable agreements were obtained. A computational model was developed for a multi-story thin steel plate shear wall subjected to cyclic loading and the results from the model were compared with experimental results, and again agreement was achieved.     

Application of ADINA to nonlinear analysis of reinforced concrete shear walls with openings

This paper is concerned with application of ADINA to elasto-plastic analysis of the shear walls with openings. The authors analyzed the types of structures. One is the shear wall with many openings (the model of a secondary shield wall in nuclear power plant), on which scale model experiments were made. The other is the shear wall with openings in concrete rigid frame (the model of a shear wall in a building), on which parametric study was made.

In both cases, concrete is modeled using 8 nodes isoparametric 2 dimensional plane stress elements, reinforcing steels are modeled as truss elements. Concrete and elasto-plastic models are adopted for non-linear material model of concrete and reinforcing steel, respectively. The total numbers of nodes are 248–308, and that of 2D elements are 66–80.

Both analytical results are satisfactory from the view point of structural design. Close agreement to experimental results in the cracking load, crack extension, elasto-plastic stiffness and total strength was verified.     

A rational model for the distortional buckling of tapered members

A general finite element is developed for the analysis of coupled local and lateral buckling of steel structures composed of tapered I-sections. Structures such as gable frames and steel bridges fall into this category. The present method is capable of considering both the tapering of the flanges as well as the web. The effect of vertical web stiffeners is handled automatically, and loading remote from shear centre can also be incorporated. The analysis is performed in two stages: in-plane and out-of-plane. The resultant in-plane stresses are used for the out-of-plane initial loading pattern. This arrangement results in a general eigenvalue problem, where the buckling load and mode are found using algorithms such as the Sturm Sequence and Random Force Vector methods. The accuracy of the method is then demonstrated in several examples incorporating tapering of both kinds. Finally, the method is used to investigate the significance of distortion in the buckling of a typical gable frame under gravity loads.     

Efficient finite element modelling of reinforced concrete beams retrofitted with fibre reinforced polymers

This paper presents a new simple and efficient two-dimensional frame finite element (FE) able to accurately estimate the load-carrying capacity of reinforced concrete (RC) beams flexurally strengthened with externally bonded fibre reinforced polymer (FRP) strips and plates. The proposed FE, denoted as FRP–FB-beam, considers distributed plasticity with layer-discretization of the cross-sections in the context of a force-based (FB) formulation. The FRP–FB-beam element is able to model collapse due to concrete crushing, reinforcing steel yielding, FRP rupture and FRP debonding.The FRP–FB-beam is used to predict the load-carrying capacity and the applied load-midspan deflection response of RC beams subjected to three- and four-point bending loading. Numerical simulations and experimental measurements are compared based on numerous tests available in the literature and published by different authors. The numerically simulated responses agree remarkably well with the corresponding experimental results. The major features of this frame FE are its simplicity, computational efficiency and weak requirements in terms of FE mesh refinement. These useful features are obtained together with accuracy in the response simulation comparable to more complex, advanced and computationally expensive FEs. Thus, the FRP–FB-beam is suitable for efficient and accurate modelling and analysis of flexural strengthening of RC frame structures with externally bonded FRP sheets/plates and for practical use in design-oriented parametric studies.     

Stability and load-carrying capacity of three-dimensional long-span steel arch bridges

The behavior of several models of three-dimensional long-span steel arch bridges is investigated for evaluating the effects of various design parameters on both the strength and stability of these special structures. The major concerns in the design of a long-span steel arch bridge, from the structural safety point of view, are the yield and buckling failures. Different design parameters may affect the failure load for either type of failure in various ways. This study investigates how changes in certain design parameters would affect the behavior of steel arch bridges, which could lead to an optimum design of this type of bridge structures. The effects of the plate girder stiffness and arch bracing stiffness as well as the rise-to-span ratio and inclination of the arches towards each other are examined in this study. Both critical buckling load and the load-carrying capacity of each design alternative are investigated using the finite element method. All design alternatives are based on the latest AASHTO code for highway bridge design. It is concluded from this study that the inclined arch bridge using the maximum practical rise-to-span ratio (which is about 0.25) is the most favorable design. In addition, the increase in the stiffness of the plate girder does not reduce the bending moments in the arch ribs. However, providing a lateral bracing system with sufficient stiffness greatly reduces the out-of-plane bending moments and increases the load-carrying capacity and the critical buckling load of a long-span arch bridge.     

Numerical simulations of oblique penetration into reinforced concrete targets

A dynamic constitutive model based on the tensile and the compressive damage models for concrete was developed and implemented into the three-dimensional finite element code, LS-DYNA. Numerical simulations of oblique penetration into reinforced concrete targets were performed using LS-DYNA. On the basis of the proposed model, the tensile and compressive damages of reinforced concrete after oblique penetration were observed and the deformation of reinforcing steel bars was obtained. Moreover, the depths of penetration for different oblique angles were obtained. The numerical results for the depth of penetration are in good agreement with existing experimental data.     

Multi field modeling of a microelectromechanical speaker system with electrostatic driving principle

The need for computer modeling tools capable of precisely simulating multi-field interactions is increasing. The accurate modeling of an electrostatically actuated Micro-Electro-Mechanical-Systems speaker results in a system of coupled partial differential equations (PDEs), describing the interactions between electrostatic, mechanical and acoustic fields. A finite element (FE) method is applied to solve the PDEs efficiently and accurately. In the first part of this paper, we present the driving technology of an electrostatic actuated Micro-Electro-Mechanical-Systems speaker, where the electrostatic mechanical coupling is realized with reduced order electro mechanical transducer elements. The electrostatic attracting force is derived from the capacity to gap relation of our device. In a second investigation, we focus on generation of the generated sound including open domain characteristics and propagation region optimization. The sound pressure level is computed with Kirchhoff Helmholtz integral as well as with FEM by using CFS++. We use the Kirchhoff Helmholtz model to characterize the interactions of multiple speaker cells in arrays and the FE tool for single speaker cell investigations. At the acoustic FE model, the focus is on mesh generation and optimization of the propagation region using non-conforming grids (Mortar FEM) and in addition at the boundary region to model open domain characteristics. We apply a recently developed perfectly matched layer technique, which allows us to truncate the acoustic propagation domain with open domain characteristics. Finally, we present an optimization method taking advantage of stress induced self-raising realized with various merged layers with different intrinsic pre-stress. The buckling back plate concept can be compared to bimetal characteristics.     

Nonlinear influence of contraflexure migration on near-curtailment stresses in hyperstatic FRP-laminated steel members

The flexural characteristics of hyperstatic steel members with adhesively bonded Fibre reinforced polymer (FRP) laminates are considered. It is shown that, during elasto-plastic activity, the migration of the points of contraflexure along such members has two nonlinear effects on the stresses in both the laminate and the adhesive. First, the lengths of laminate traversed by these migrating points undergo reversal of axial stress from tension to compression, which exposes the laminate to potential buckling. Second, the bond stresses in the adhesive near laminate curtailment increase dramatically, and so may initiate brittle failure near curtailment by separation of the laminate from the steel member. Nonlinear finite element (FE) analyses are used to illustrate both these effects. The FE model is verified by comparison with published data, and is then used to analyse an isostatic and a hyperstatic FRP-laminated steel member. The results show that the above nonlinear influences are pronounced in the hyperstatic member, but are absent from the isostatic member. Tapering of both the laminate and adhesive profiles near curtailment of the laminate is investigated as a potential means of reducing these effects in the hyperstatic member. Finally, the implications of the above effects for the performance of hyperstatic FRP-laminated steel members in practice, are discussed.     

A computational and experimental analysis of the buckling,postbuckling and initial failure of pultruded GRP columns

A two-dimensional finite element (FE) model was developed and nonlinear FE analyses were carried out, using the ANSYS software, to predict the buckling, postbuckling and initial failure loads of pultruded glass reinforced plastic (GRP) wide flange (WF) columns. Phenomenological failure criteria were proposed to predict failure initiation at the web-flange junctions of pultruded GRP WF columns, whereas the Tsai–Wu failure criterion was used for the web and flanges. Initial failure analysis was carried out with reasonable success as a post-processing operation on the nonlinear analysis results. The numerical predictions of the buckling, postbuckling and initial failure loads of pultruded GRP WF columns were in reasonably good agreement with the experimental results.     

Analytical Model for Analysis and Design of V-Shaped Thermal Microactuators

An analytical solution of the thermoelastic bending/buckling problem of thermal microactuators is presented. V-shaped beam actuators are modeled using the theory of beam-column buckling. Axial (longitudinal) deformations including first-order nonlinear strain-displacement relations and thermal strains are included. The resulting nonlinear transcendental equations for the reaction forces are solved numerically and the solutions are compared with a nonlinear finite element (FE) model. A test actuator has also been fabricated and characterized. The obtained accuracy of the prediction is within 1.1% of the nonlinear FE solution and agrees well with the experimental data. A corresponding one-dimensional (1-D) heat transfer model has also been developed and validated against experimental$i$-$V$measurements at various temperatures. The developed analytical models are then used to analyze maximum stress and the heat transfer paths. It has been confirmed that the heat flux toward the substrate is a dominant heat dissipation route in sacrificially released devices.hfillhbox[1311]     

Optimum design and evaluation of stiffened panels with practical loading

Optimum design of a blade-stiffened panel of composite/honeycomb sandwich construction and a metal T-stiffened panel is considered using the buckling and strength constraint program VICONOPT. Both panels have practical loadings which produce a nonlinear out-of-plane bending moment, calculated using beam-column expressions. Large deflection finite element analysis of the optima shows that modifications to these expressions are necessary when the panels are shear loaded. The use of integrally machined stiffeners, as opposed to a conventional, built-up panel designed using PANDA2, is shown to permit 20% mass saving when the latter has no postbuckling strength and 3% saving when postbuckling strength is allowed for.     

Design and Characterization of Single-Layer Step-Bridge Structure for Out-of-Plane Thermal Actuator

This paper presents the design and fabrication of a single-layer out-of-plane thermal actuator. The step-bridge structure design enables bending and then buckling of the actuator in the out-of-plane direction by Joule heating. Moreover, the moving direction of the actuator can be specified by the step structure. In summary, the step-bridge actuator design has the following five merits: (1) The load-deflection relation is easily tuned; (2) the bistable buckling behavior is prevented; (3) the unwanted vibration modes can be suppressed; (4) the delamination problem is prevented; and (5) the bridge structure is stiffer and more stable. The actuator and its application on a lens positioning stage have been implemented using p⁺⁺ Si layer by bulk micromachining. It demonstrates that a typical actuator would move upward with an amplitude near 13 mum when driven at 54 mW.     

An efficient generation method of embedded reinforcement in hexahedral elements for reinforced concrete simulations

In this paper, an automatic procedure for the generation of embedded steel reinforcement inside hexahedral finite elements is presented. The automatic mapping of the entire reinforcement network inside the concrete hexahedral finite elements is performed using the end-point coordinates of the rebar reinforcement macro-elements. By introducing a geometrical constraint, this procedure decreases significantly the computational effort for generating the input data of the embedded rebar elements in three-dimensional finite-element analysis, particularly when dealing with relatively large-scale reinforced concrete models. The computational robustness and efficiency of the proposed mesh generation method are demonstrated through numerical experiments.     

Propagation of a cohesive crack through adherent reinforcement layers

This paper analyzes the propagation of a cohesive crack crossing one or several reinforcement layers by a simple model valid for any specimen or loading condition. In this instance the case of reinforced concrete beams loaded at three points is considered. In this approach steel bars do not constitute a physical barrier to the propagation of the crack, as concrete continuity is preserved by a computational strategy consisting of overlapping both materials in the same spatial position. The model uses cohesive elements to represent the crack and interface elements to simulate the decohesion and shear generated in the steel-concrete debonding process. The results given by this model are compared to experimental results on rectangular and T-shaped beams reinforced by bars arranged in one or several layers. The model closely follows the experimental trends when changing the parameters that control the type of fracture; such as the steel ratio, the bond strength, the position and arrangement of the bars, the size of the specimen and the shape of the beam cross-section. In spite of its simplicity, this model can be useful when studying local fracture and decohesion phenomena wherever they may take place within a reinforced or prestressed concrete structure.     

Computational biomechanical modelling of the lumbar spine using marching-cubes surface smoothened finite element voxel meshing

There is a need for the development of finite element (FE) models based on medical datasets, such as magnetic resonance imaging and computerized tomography in computation biomechanics. Direct conversion of graphic voxels to FE elements is a commonly used method for the generation of FE models. However, conventional voxel-based methods tend to produce models with jagged surfaces. This is a consequence of the inherent characteristics of voxel elements; such a model is unable to capture the geometries of anatomical structures satisfactorily. We have developed a robust technique for the automatic generation of voxel-based patient-specific FE models. Our approach features a novel tetrahedronization scheme that incorporates marching-cubes surface smoothing together with a smooth-distortion factor (SDF). The models conform to the actual geometries of anatomical structures of a lumbar spine segment (L3). The resultant finite element analysis (FEA) at the surfaces is more accurate compared to the use of conventional voxel-based generated FE models. In general, models produced by our method were superior compared to that obtained using the commercial software ScanFE.     

基于ANSYS的角钢局部屈曲/后屈曲等效分析

将角钢等效成简单板材,通过分析其屈曲／后屈曲来等效研究角钢的局部屈曲／后屈曲．采用ANSYS严格按照角型材实际尺寸建立三维实体模型,并进行屈曲／后屈曲数值模拟．三维有限元解与理论等效结果符合良好,充分说明该等效分析的正确性和适用性．     

Lay-up optimization for the hull of a racing sailing yacht

Deformability and buckling load of yacht hulls with fiber reinforced plastic sandwich structure depend on the stack sequence of the skins. In this work an optimization of fiber directions of the laminae for a racing yacht is proposed.This procedure has been divided into three parts (i.e. material characterization, surface model definition, lay-up optimization). First of all a set of unidirectional specimens has been realized, by using the same fibers and matrix (carbon/epoxy) used for the hull as well as the same procedure and workers, in order to characterize the material according to American Society for Testing and Materials (ASTM) Standard D3039, employing strain gage technique. In the second part, by means of an original software in Turbo-Pascal (which uses the half-width value matrix as an input) linked to Pro/ENGINEER, it has been possible to obtain the body plan and surface and finite element (FE) models of the sailing yacht for the subsequent analyses. In the third step, an optimization procedure that uses the results of FE structural analyses in three different sailing configurations is performed, with the aim of obtaining the fiber directions that are able to minimize the yacht deformability, also taking into account the buckling loads. An approximate analytical model has been used in conjunction with a sweep technique in order to evaluate the best of the solutions.     

Elastic lateral torsional buckling of unbraced and braced planar frames

A general finite element formulation to obtain lateral-torsional buckling solution of braced and unbraced planar structures loaded in-plane, is presented. The effects of in-plane deformations on lateral-torsional buckling are included. In-plane deformations are determined by following the loading path in incremental steps, through a series of equilibrium states and the critical load is found by determining the point at which the determinant of stiffness matrix of out-of-plane deformations becomes zero. The validity of the formulation is verified by testing for convergence and comparing the solutions with available results. The behaviour of unbraced and braced frames are investigated using this formulation.