Plate-type Structures Research Articles

The buckling of composite stiffened box sections subjected to compression and bending

In this paper a study is made of the buckling characteristics of some carbon fibre composite stiffened box sections when subjected to compressive and bending loading actions. The results presented have been determined through the use of the finite strip method of analysis. This method of approach has become popular in its application to thin-walled prismatic plate type structures. Such structures are easily modelled using thin flat strips and considerable flexibility can be readily built into the model with the most appropriate choice of strip formulation. The structural box sections considered are manufactured from high strength carbon-epoxy long fibre composite material and are stiffened longitudinally by plain flat outstands attached to the inner surfaces of the walls of the sections. The skin and stiffeners of the box sections are manufactured from pre-impregnated ply sheets and have a symmetric cross-ply lay-up configuration. The effect of variation in stiffener depth on buckling response is examined in some detail. It is shown that very moderate stiffener dimensions can substantially improve the buckling capability of the box sections. The buckling mode shape is shown to depend significantly on the stiffener depth. For the smaller stiffener depths the mode of buckling is general in nature, involving considerable in-plane bending and twisting of the stiffener. Local buckling is enforced for the larger stiffener depths and this may be skin or stiffener initiated depending on stiffener size. The flexibility and versatility of the finite strip method in being able to pick up the different buckling modes associated with geometry changes is clearly demonstrated in the paper. In particular, the relative ease with which the finite strip method can accommodate changes in material properties and structural geometry permits the close examination of a wide range of the design variables and thus more efficient structural components can be realised. Optimised stiffener depths with regard to buckling of the composite box sections are indicated in the paper for the individual loading cases of compression and bending.

AN ASSESSMENT OF THE EFFECTS OF IN-PLANE VIBRATIONS ON THE ENERGY FLOW BETWEEN COUPLED PLATES

The majority of the studies of energy transmission in plate-type structures are based on the assumption that the main component of the energy transfer is due to flexural waves, and the contribution of in-plane waves may be neglected. In this study a systematic assessment of the effects and importance of in-plane vibrations has been made by using the dynamic stiffness technique which yields “exact” results for a certain class of structures. The method is also used as a “bench-mark” to assess the predictions of the statistical energy analysis (S.E.A.) approach and the wave intensity analysis (W.I.A.) approach. It is shown that the exclusion of in-plane modes may lead to sizeable errors in energy predictions unless the structure is very simple.

Computing critical points and secondary paths in nonlinear structural stability analysis by the finite element method

Stability analysis is a crucial aspect of structural design, particularly for beam, plate and shell type structures. The stability of a structure is often governed by singular points in its equilibrium path. These points usually pose serious problems to ordinary finite element solution methods and require special treatment. In this paper, the state-of-the-art of finite element path-following techniques is critically reviewed with special attention to bracketing procedures for the singular points and branch switching algorithms. Some practical aspects involved will be explained in detail and demonstrated through numerical examples at the end.

Analysis of clamped rectangular orthotropic plates subjected to a uniform lateral load

The increasing use of composite materials for plate-type structures intensified the need for solutions of orthotropic plates. One problem of interest is the clamped rectangular plate with reinforcing fibers parallel to the plate boundaries. There is no exact analytical solution for this problem. The purpose of this paper was to derive a closed-form approximate solution of high accuracy, even for third derivatives (shearing forces). This was achieved by utilizing the extended Kantorovich method. It was found that the convergence of this procedure is very rapid, in that the final form is reached after only four iterations, and that the final form of the generated solution is independent of the initial choice. To establish the accuracy of this solution, it was numerically evaluated for a plate made of Kevlar 49 Epoxy, and the results obtained were compared with the corresponding results by Whitney [Structural Analysis of laminated Anisotropic Plates. Technomic, Lancaster; Pennsylvania (1987)], as well as with the exact solution for a clamped infinite strip. It was found that with increasing plate aspect ratios, the deflections and bending moments generated approached closely those of the infinite strip, but those of Whitney did not.

Exact solutions for static analysis of intelligent structures

Exact solutions for static analysis of simply supported rectangular plate-type intelligent structures are presented. The intelligent structure proposed here is composed of a laminated substrate of graphite/epox y composite coupled with distributed sensor and actuator layers of a biaxially polarized piezoelectric polymer, polyvinylidene fluoride (PVDF). The study aims at investigating the capability of the actuator and sensor layers to cause and sense the deformations, respectively, of the substrate of the intelligent structure. The results show that the effectiveness of the piezoelectric actuator layer to cause induced strain actuation in the structure significantly increases with the decrease in the length to thickness ratio of the substrate.

Dynamic Peripheral Milling of Flexible Structures

A dynamic model for peripheral milling of very flexible plate type structures has been presented. The structural dynamics of a cantilevered plate structure is modelled at the tool-workpiece contact zone. The interaction of the very flexible plate structure and rigid end mill during dynamic milling is modelled. The variation in surface, chip thickness, and structural dynamics of the plate are considered in determining the milling forces. The proposed model provides surface finish form errors displacements at the tool-workpiece contact zone, and cutting forces for dynamic end milling operations.

Definition of hot spot stress in welded plate type structure for fatigue assessment (1st Report)

In design of a large marine structure, the assessment of fatigue strength is one of major design considerations. In evaluation of fatigue strength of welded toes, it is important to analyze the “hot spot stress” due to structural discontinuity accurately but in a single way.The hot spot stress will be defined as a conventional stress at an intersection of plates where fatigue crack is possibly expected to occur.For plate type structures, it is not clear how to define the hot spot stress.In this paper, using the experimental data of the model tests carried out by SR202 committee of Shipbuilding Research Association of Japan, a definition of the hot spot stress and S-N diagram for fatigue design of plate type structures were proposed.The hot spot stress for plate type structure is defined by linear extrapolation of measured strains with the location at distances of two points to the welded toe. The two points are 1.574/√ (T3) and 4.94√ (T3), where design S-N diagram in term of the hot spot stress is newly defined named as SRF curve.

Model fatigue test result of welded structural element and proposal for fatigue design procedure

For carrying out the fatigue design of welded structures, the design S-N diagram to be used may be prepared either by the joint classification method or by the hot spot stress method. The former has a long history in design of bridge, but it is not so clear how to select the S-N diagram in design of a large marine structure using nominal stress or hot spot stress.In this paper, using the experimental data of the model tests which have been carried out by SR202 Committee of Shipbuilding Research Association of Japan, proposal for fatigue design procedure of plate type structures (bracket, stiffener and doubler pad connections) was discussed.

Definition of hot spot Stress in welded structure for fatigue assessment (2nd Report)

In design of a large structure, the assessment of fatigue strength is one of major design considerations. In evaluation of fatigue strength of welded toes, the development of FE analysis and detailed model tests have enhanced the use of “Hot Spot Stress” or “Peak Strain” concepts.In the first report, the hot spot stress definition for plate type structures was discussed, using the experimental data of the model tests by SR202.In this paper, fatigue strength assessment in the use of “Peak Strain” concept is presented. Fatigue strength assessment methods with the peak stress are shown in ASME Boiler and Pressure Code Sec. III and NK rule Part P.For the short of TMCP steel low cycle fatigue data and the short of application for model tests data in the peak strain concept application, in this research, low cycle fatigue tests of round bars with notch were done and analysis based on the peak strain concept for the model tests by SR202 have been made.In the analysis, the NK method with some choice of detailed assessment process have been investigated.Finally, detailed calculation method for the peak strain with the object of assessing low to high cycle fatigue strength of welded structures is proposed, that is the use of Neuber rule for plastic strain concentration and Manson method for stable stress strain relation.

Spline compound strip analysis of folded plate structures with intermediate supports

A B-spline column element in 3D space is derived and combined with the B- spline compound strip method for the analysis of plate-type structures (e.g. folded plates, box-girders, etc.) with intermediate supports. A direct stiffness method is used. Numerical examples demonstrate the advantages of this method: accuracy, efficiency and simplicity.

Hydrostatic loading and stability analysis of structures with large displacements

AbstractA method for the computation of hydrostatic forces on cable, truss, beam, plate and shell type structures is presented. A general large displacement formulation is assumed which allows for displacements and rotations of unlimited size. Equilibrating forces for nodal points as well as incremental force‐displacement relationships are given. Various ways of making the geometric load matrix symmetric for incremental analysis is discussed. Alternative strategies for the incremental–iterative solution is also treated. A method for the determination of the hydrostatic stability of floating structures is suggested. Metacentres and centres of buoyancy for rotations about principal axes in the water plane are automatically computed. The paper presents three examples of applications: a pipe which is partially submerged, a full overturning of a floating space frame and, finally, a hydrostatic stability analysis of a ship.

Through‐the‐thickness stress predictions for laminated plates of advanced composite materials

AbstractA finite element formulation is developed with emphasis primarily focused on providing stress predictions for thin to moderately thick plate (shell) type structures. Plate element behaviour is specified by prescribing independently the neutral surface displacements and rotations, thus relaxing the Kirchhoff hypothesis. Numerical efficiency is achieved due to the simplicity of the element formulation, i.e. the approach yields a displacement dependent multi‐layer model. In‐plane layer stresses are determined via the constitutive equations, while the transverse shear and short‐transverse normal stresses are determined via the equilibrium equations. Accurate transverse stress variations are obtained by appropriately selecting the displacement field for the element. A selective reduced integration technique is utilized in computing element stiffness matrices. Static and spectral (eigenvalue) tests are performed to demonstrate the element modelling capability.

Attitude Dynamics of a Satellite During Deployment of Large Plate-Type Structures

The paper analyzes the attitude dynamics of a spacecraft while deploying large plate-like structures. Equations governing the rotational dynamics of the system and the lateral vibrations of the panels are obtained using a Lagrangian formulation. Even the linearized equations are unusually lengthy and involve time-varying coefficients. Hence they are integrated numerically for given length histories. Two types of axial extension—uniform and exponential—are considered. The system parameters are varied for the two procedures and their influence on the attitude dynamics is noted.

A high precision triangular laminated anisotropic cylindrical shell finite element

The stiffness matrix for a high precision triangular laminated anisotropic cylindrical shell finite element has been formulated and coded into a composite structural analysis program. The versatility of the element's formulation enables its use in the analysis of multilayered composite plate and cylindrical shell type structures taking into account actual lamination parameters. The example applications presented demonstrated that accurate predictions of stresses as well as displacements are obtained with modest number of elements.

The damping of plate vibration by interfacial slip between layers

The damping on plate type structures can be significantly increased by using laminated plates correctly fastened to allow controlled interfacial slip during vibration. The clamping forces acting on a laminated plate to give maximum damping and minimum response amplitude have been investigated for the first mode of plate vibration. The optimum clamping force required for maximum damping has been found to be less than that required for minimum response, but in both cases the magnitude of these forces have been found to be dependent on the exciting force. Clamping forces within the range of these optima reduce the response amplitude by about 70%. A theoretical analysis which modelled the laminated plate as a single plate subjected to in plane forces is presented; good qualitative agreement with the experiment was found.

On the accuracy of model testing

In this article an attempt is made to estimate the effects of some factors on the accuracy of results of model tests. As an example an analysis was performed upon the investigations on plate-type bridge structures made in the Bridge Department of the Technical University of Wroclaw (Politechnika Wroclawska) Poland. The methods of the model testing, errors in measurements resulting from the in-series connection of electrical extensometers of different initial resistances, as well as errors caused by inaccuracies in positioning extensometers on the model are discussed. Finally the effect of inaccuracies in measuring thicknesses of the model plates is estimated and the total error of the bending or twisting moment computed from the influence surfaces, as determined in model tests, is found.