Modal Analysis of General Plate Structures

Adequate asymptotic treatment of the double diffraction by a pair of parallel edges in the overlapping transition regions requires a spectral integral representation of the singly-diffracted field. Such a representation is derived here for the diffraction by a convex cylinder. This enables one to extend the solutions for the double-edge diffraction to the case of two parallel convex cylinders, or of a cylinder parallel to an edge.

We have developed a hybrid method applicable to straight-crested waves in arbitrary anisotropic crystal plates and to axisymmetric piezoelectric vibrations in ceramic disks. The solutions to two-dimensional (2-D) equations of motion are described with a linear combination of eigenmodes guided by a pair of parallel edges. The guided eigenmodes and their amplitudes are determined by using one-dimensional (1-D) finite element method (FEM). The method developed here provides rapid convergence with small matrix size compared with 2-D FEM. Computer programs have been developed for three examples, SC- and AT-cut quartz plates and barium titanate (BaTiO/sub 3/) disks, for which the frequency spectra and the corresponding mode shapes were calculated. The frequency spectra of AT-cut quartz plates are compared with those obtained from Mindlin's plate equations, with the aim of examining the accuracy of the straight-crested wave solutions for Mindlin's plate equations. A convergence study is also presented for BaTiO/sub 3/ disks.

The boundary conditions of basic load support structures formed by beam elements are neither purely simply supported nor clamped that can be termed as conventional. It has certain finite rotational and translational stiffness representing an intermediate state (a welded end/riveted structures to name a few). The conventional methods of separation of variables for beam vibration analysis have not found substantial applications for boundary conditions which are not conventional. The paper attempts to bring out the effect of variation of the end supports, in terms of variation in translational and rotational stiffness, on the vibration characteristics of a beam element in terms of frequency and mode shapes. Fourier sine series approximation has been used for theoretical evaluation. Numerical assessment has been undertaken on an I-beam. Variable stiffness has been accounted for by using variable elastic end conditions and results on frequencies and mode shapes of the I-beam have been presented.

Analytical models for load capacities of variable thickness reinforced concrete slabs considering compressive membrane action and boundary effects

The thesis presents a theory for the bending of laser-welded web-core sandwich plates. The sandwich plate theory and homogenization are utilised, enabling a similar, fairly coarse, FE mesh to be used for design alternatives with different cross-sectional dimensions. This is considered to be beneficial during the design, when different alternatives should be evaluated. The thesis also studies the main factors that contribute to the total bending response of laser-welded web-core sandwich plates.\n\nThe actual periodic structure is homogenized, giving equivalent stiffness properties for the sandwich plate. The differential equations for this homogenous sandwich plate, with thick face plates, consist of those for displacements of the well-known Reissner-Mindlin and Kirchoff plate theories. Therefore, the solution of these differential equations can be carried out using commercial Finite Element software. The periodic structure is reconsidered when the stress formulations are derived. The approach is validated with Finite Element calculations based on actual 3D topology.\n\nThe rotation stiffness of the laser stake welded T-joint between the web and face plate is derived experimentally. This is considered to be important since the rotation stiffness affects the shear stiffness in the opposite direction to that of the web plate. An experimental procedure for the determination of the T-joint rotation stiffness is developed and validated. The mechanics of the T-joint are investigated with Finite Element analyses.\n\nThe moment introduced by the web plate to the face plate is very important when deflections and normal stresses are considered. This moment is affected by the stiffnesses of the web plate and the T-joint. The deflections are significantly increased by a decrease in the web plate or T-joint rotation stiffness. The influence is greatest with cross-sections where the face plate thickness is large and the web plate spacing is small. Plates with a low aspect ratio under a uniform pressure load have the same maximum deflection, regardless of the T-joint rotation stiffness. Contrary to this, plates with a high aspect ratio or a patch load on a small area are very sensitive to rotation stiffness. The periodicity of the structure is found to have a significant influence on normal stresses in the face and web plates. Because of homogenization shear-induced, periodic, normal stresses vanish. In actual structures these stresses can be an order of magnitude higher than those induced by the bending moments of the sandwich plate. Therefore, the periodic structure as presented in this thesis should be taken into consideration when the normal stresses are calculated. Patch loads on a very small area can cause normal stresses even higher than those induced by shear. The web plate thickness is found to have a significant influence on stresses, but in the measured range of T-joint rotation stiffness values, the stresses are found to be unaffected.

Analysis of lateral instability of in-plane comb drive MEMS actuators based on a two-dimensional model

Bending analysis of a functionally graded circular plate with clamped and simply supported boundary conditions is carried out. Material properties of the plate are assumed to be functionally graded in two directions, namely in the radial direction and through the thickness of the plate, obeying exponential distribution laws. Poisson’s ratio is assumed to be constant throughout the plate. Governing equations of a circular plate with material properties varying only through the thickness of the plate, based on the third order shear deformation theory are employed. In order to carry out the bending analysis of a two directional functionally graded circular plate, the plate is divided into number of annular plates with material properties graded only through the thickness. Material properties of each annular plate are defined by the corresponding exponential grading rule and the radial position of its center, hence these properties are assumed to be constant for each annular plate but different from its adjacent plates. Imposing the overall boundary conditions and compatibility conditions of adjacent annular plates, the governing equations of all annular plates are obtained and solved simultaneously. The analytical results are compared with the results obtained by the first order shear deformation theory and finite element method which are found to be in good agreement.

The prediction of the behaviour of Spatial joint and plane joint relied on experimental and numerical tests that provide accurate information for the characterization of the beam to Column connection with T-stub. The corner column connections of steel frame as the research object and there are one spatial T-stub connection specimen and one plane T-stub connection specimen. Spatial cyclic load of quasi-static tests and finite element analysis were carried out, of which load was applied to the column. According to the results of quasi-static tests and finite element calculations, difference of joints’ rotational stiffness, hysteretic property, ductility coefficient and energy dissipation characteristics were analysed. It is verified that the mechanical characteristics of spatial semi-rigid joint under spatial load are different from plane semi-rigid joint under plane load.

A codecheck methodology, suitable for checking the behaviour of stiffened steel plate structures, is proposed in this paper. The methodology adopts the most appropriate, complementary aspects of existing codes, supplemented by pertinent recent research. A case history of the Beryl Alpha platform is presented. This demonstrates the benefit of applying the methodology to the post processing of a finite element analysis of the deck. With minimal, but effective stiffening, an overall 17% increase in deck load is now carried. The additional capacity was used for safety enhancements and improvements necessary to extend the platform's economic life. INTRODUCTION Although code checking of framed and simple plated structures (e.g. large diameter stiffened tubulars) is normally highly automated, the opposite is true of complex stiffened plate structures. Such construction is commonplace in the offshore industry; it is featured in modules, plate girders, semi-submersibles, jack-ups, TLPs and tankers/FSUs. The behaviour of these structures is less well understood thanthat of framed structures due to the great variety of possible load paths and failure mechanisms. Development of a unified set of rules describing the behaviour of the components of complex plated structures has yet to be concluded. This leaves the offshore industry in an unenviable position. At a time when considerable attention is being paid to the intrinsic safety of such structures, the codes of practice are lagging behind the state-of-the art knowledge embodied in recent research. To overcome this limitation, it is possible to combine the best features of existing codes/rules/standards together with the published or even unpublished results of this research. The code check methodology described in this paper is justsuch a combination. It covers strength, serviceability and fatigue limit states and is particularly suited to the post processing of finite element (FE) analyses. One particular example of stiffened plate construction is the deck of Beryl Alpha. This platform, installed in 1975, comprises a three legged concrete substructure supporting the topsides structure and equipment. The platform is operated by Mobil North Sea Limited (MNSL); the other coventurers are Amerada Hess Limited, Enterprise Oil plc, B.G. North Sea Holdings Ltd and OMV (UK) Ltd. Due to the continuing research and development of various codes of practice and improvements in FE analysis capability since the Beryl Alpha design, MNSL believed that there wasconsiderable scope for increasing the allowable deck load on the platform. A number of upgrades to the platform were planned between 1988 and 1992 and consequently an additional 5,000 tonnes have now been added. The integrity of the structure under this new loading was demonstrated using detailed FE analysis and the above codecheckmethodology. This paper is organised with a review of formal codes and rules followed by the development of appropriate strength and buckling check methodologies and their computerimplementation. A description of the application of the techniques to Beryl Alpha and a discussion of the results complete the paper.

Application of boundary-domain element method to the free vibration problem of plate structures

The forces and/or moments applied to a ball joint and a bushing in one suspension are important loads for the design or fatigue tests of control arms, trailing bars and steering knuckles. Taking a double wishbone suspension as one studying example, a modeling and calculation method for obtaining the forces applied to the ball joints and the bushings, and moments applied to the bushings are proposed and developed in this article. In modeling of a suspension, a bushing is modeled with three translational stiffness and three torsional stiffness along and around three orthogonal axes. The force (moment) versus displacement (angle) along (around) one axis is nonlinear and is simplified as piecewise linear at five sections. The joint forces and moments for ball joints and bushings of a double wishbone suspension system are calculated with the proposed method in this article, and compared with that obtained using two conventional methods (method I and method II) when a vehicle runs in typical and extreme driving conditions. Conventional method I simplifies the connections between the control arm and body as rigid link. Conventional method II assumes that the control arm links with the body using bushings, in which the bushings are modeled as three linear stiffness along three orthogonal axes. The calculation and comparison demonstrate that the bushing nonlinear and rotational stiffness must be modeled for precise calculation of ball joint force and moments, especially when a vehicle runs in extreme driving conditions.

Modelling of thermal expansion of single- and two-phase ceramic polycrystals utilising synthetic 3D microstructures

Objective To evaluate the biomechanical characteristics of 4 fixation methods (single reconstruction plate, dual reconstruction plates, single cannulated screw and dual cannulated screws) in the treatment of pubic symphysis disruption. Methods Miniature spiral CT scans were performed on the complete pelvis in 5 healthy volunteers. The primary two-dimensional CT scan data at DICOM format were imported into software Mimics 15.0 for three-dimensional reconstruction of bilateral hips and sacrums. The finite element model of skeletal pelvis was obtained by grid partitioning and assignment using software Abqus 6.13. Models of pubic symphysis disruption were simulated by cutting off the unilateral sacroiliac ligament, sacral spine ligament, sacral tuberosity ligament, pubic ligament and pubic arch. Four implants(single reconstruction plate, dual reconstruction plates, single cannulated screw and dual cannulated screws) were simulated and emplaced onto the models according to standard surgical procedures. Compressive and rotational loads were implemented in all models for finite element analysis. The biomechanical properties were recorded and analyzed, including construct stiffness, micromotion of the pubic symphysis and von Misses stress. Results Under vertical load, the space of pubic symphysis disruption >25 mm. The vertical stiffness and rotational construct stiffness of the pelvis decreased significantly from 442.738±29.946 N/mm and 10.118±1.432 N·m/Deg in the normal group to 14.754±0.876 N/mm and 0.328±0.119 N·m/Deg, respectively. Dual reconstruction plates and dual cannulated screws displayed the best vertical tensile strength; their construct stiffness achieved 117.647±9.193 N/mm and 131.443±4.348 N/mm, respectively. Under anti-rotation load, dual cannulated screws displayed the best performance because they rebuilt 68.6% of the whole structural stiffness. For the local stability of the pubic symphysis, dual reconstruction plates showed a strong local anti-rotation capability and dual cannulated screws a good local anti-tensile capability. The displacement in the dual cannulated screws group was only -0.240±0.119 mm under vertical load while the angular displacement in the dual reconstruction plates group only 0.218°±0.182°. Single reconstruction plate endured the maximum von Misses stress which was obviously concentrated. Conclusion Dual cannulated screws may have biome-chanical advantages for treatment of pubic symphysis disruption. Key words: Pelvis; Finite element analysis; Biomechanical characteristics; Fractures fixation, internal; Comparative study

Stress-driven nonlocal integral model with discontinuities for transverse vibration of multi-cracked non-uniform Timoshenko beams with general boundary conditions

Free vibration of the complex cable system − An exact method using symbolic computation