Thermal bending of thin, anisotropic, clamped elliptic plates

The present note deals with the exact analytical solution of thermal bending of clamped, anisotropic, elliptic plates in the case where the thermal field is given by an expression of the type T(x,y,z)=z(Ax²+Cxy+By²).The problem is of basic interest in some ocean and mechanical structural systems since anisotropic materials are commonly used in those fields. Obviously the case of an orthotropic material constitutes a particular situation of the problem under study.     

The hydrodynamics of thin floating plates

The radiation and diffraction problems are considered in the frequency domain for a thin elastic plate of rectangular planform floating in an irrotational, incompressible ocean of infinite depth. The inner potential field inside a hemisphere surrounding the plate is represented using a spherical harmonic expansion which suits the geometry and zero-draft nature of the plate. Problems associated with distributing sources in the free surface are avoided. The Chen and Mei variational principle is used to weakly match this inner solution and its normal derivative to an outer field described by distributing sources on the exterior of the hemisphere. The validity of the procedure is first illustrated by considering a heaving circular disk. Numerous hydrodynamic coefficients are presented as benchmark data for floating flexible structures. The transient motion of the plate is simulated using rational approximations (in the frequency domain) to the radiation impedance and diffraction mapping which are implemented as ODE's in the time domain.     

Hydrodynamic shape optimization of thin floating plates

In this work, the problem of optimizing the shape of a thin floating plate (sometimes called a dock) to maximize radiation damping is investigated. The plate is modeled with zero draft and floats on the surface of an irrotational, incompressible ocean of infinite extent. For simplicity, only rigid heave motions are considered. The flow problem is analyzed using the Chen and Mei variational principle wherein the potential field inside a hemisphere surrounding the plate is represented using a spherical harmonic expansion and matched on the hemisphere to an outer field described by distributing sources on the hemisphere. The plate shape is parameterized using a Fourier series which is suitable for use with the variational principle. Gradients of the damping coefficient with respect to the shape parameters are developed by solving an adjoint flow problem whose potential is shown to be a scalar multiple of the original flow potential. Optimal plate shapes are determined using the well-known optimization code NPSOL which makes use of the damping coefficient calculation and gradients.     

Analysis of vibrating, thin, rectangular plates with point supports by the method of differential quadrature

The title problem is solved by an approach first suggested by Bellman early in the 1970s and which has recently been used in the solution of solid mechanics problems. It is shown that the methodology offers several important advantages from the point of view of naval analysts and designers.     

Oscillating inviscid flow over elliptic cylinders with flat plates and circular cylinders as special cases

The problem of oscillating inviscid flow over an elliptic cylinder is studied for various angles of attack. The flow is incompressible and two-dimensional and the oscillations are harmonic. The flow direction is always normal to the cylinder axis and oscillations are only allowed in the magnitude of the free stream velocity. The study focuses on the hydrodynamic forces acting on the cylinder as well as the surface pressure distribution and their time variation. The parameters involved are the cylinder axis ratio, the angle of attack and the Strouhal number. The variables are normalized in such a way that the solutions for the problems of oscillating flow over flat plates and circular cylinders can be easily obtained as special cases. Analytical expressions are given for the drag coefficient, the lift coefficient, and the surface pressure distribution and their variation with time. Similar analytical expressions are given for the special cases of circular cylinders and inclined flat plates in oscillating inviscid flows.     

Thermal entanglement in two-qutrit spin-1 anisotropic Heisenberg model with inhomogeneous magnetic field

The thermal entanglement of a two-qutrit spin-1 anisotropic Heisenberg XXZ chain in an inhomogeneous magnetic field is studied in detail. The effects of the external magnetic field (B), a parameter b which controls the inhomogeneity of B, and the bilinear interaction parameters J_x=Jy≠Jz on the thermal variation of the negativity are studied in detail. It is found that negativity N decreases when the values of magnetic field, inhomogeneity b and temperature are increasing. In addition, N remains at higher temperatures for higher values of J_z and lower values of B and b.     

An approximated method for the solution of elliptic problems in thin domains: Application to nonlinear internal waves

Realistic numerical simulations of nonlinear internal waves (NLIWs) have been hampered by the need to use computationally expensive nonhydrostatic models. In this paper, we show that the solution to the elliptic problem arising from the incompressibility condition can be successfully approximated by a few terms (three at most) of an expansion in powers of the ratio (horizontal grid spacing)/(total depth). For an n dimensional problem, each term in the expansion is the sum of a function that satisfies a one-dimensional second-order ODE in the vertical direction plus, depending on the surface boundary condition, the solution to an n-1 dimension elliptic problem, an evident saving over having to solve the original n-dimensional elliptic problem. This approximation provides the physically correct amount of dispersion necessary to counteract the nonlinear steepening tendency of NLIWs. Experiments with different types of NLIWs validate the approach. Unlike other methods, no ad hoc artificial dispersion needs to be introduced.     

A comparative experimental study on the blast-resistant performances of single and multi-layered thin plates under close-range airblast loading

The performance of multilayered thin steel plates subjected to close-range air blasts has been experimentally studied and compared with that of monolithic plates made of the same material and having equal mass. In present experiments, multilayered plates are in-contact four-layered thin steel plates and two types of deformation/failure modes were observed for them. Comparisons concerning deformation/failure modes, strain distributions and energy absorptions between the multilayered plate and its monolithic counterpart were conducted. It is found that the multilayered plate is much superior to its monolithic counterpart in the ability to deform against blast loading. Furthermore, under intense airblast loading, the multilayered plate can not only absorb much more energy but also effectively reduce the secondary destruction ability of structural fragments in comparison with its monolithic counterpart.     

Buckling of circular, annular plates of non-uniform thickness

This paper deals with the solution of the title problem in the case where the outer boundary is subjected to uniform, hydrostatic pressure while the inner edge of the plate is free. It is assumed that the plate thickness varies (a) in a discontinuous fashion and (b) linearly.An approximate approach is proposed using polynomial coordinate functions which identically satisfy the boundary conditions at the outer edge, only. The eigenvalues are determined using the optimized Rayleigh-Ritz method and good engineering agreement is shown to exist with buckling parameters obtained by means of a finite element code.     

Kirsch problem and the lower natural frequencies of a clamped square-plate

A clamped square-plate is subjected to a uniform state of stress in the x-direction. The present study deals with the basic question of determining the variation of the lower natural frequencies of transverse vibration of a plate as a small diameter, central hole is made in it, introducing a stress concentration field.     

基于半数值方法的限弯器剪弯刚度分析

柔性管缆限弯器存在接触非线性导致剪弯刚度分析困难。为此先基于悬臂梁方程建立剪弯刚度理论模型;然后构建考虑接触边界的锁合结构数值模型,得到其扭转刚度曲线;最后结合理论分析和数值计算求得考虑接触非线性的限弯器剪弯刚度曲线,并同传统的整体数值方法相比较,验证该半数值分析方法的有效性。对比发现基于半数值方法的限弯器剪弯计算效率远高于传统数值方法,其结果误差也满足工程需求;并且限弯器锁合结构处受接触边界影响有明显的非线性;限弯器子梁这一短梁结构基于Timoshenko梁理论计算的结果精度更高也更保守。相较于传统数值方法,该半数值方法用方程直接表达部分参数与剪弯刚度关系,并可以高效地分析限弯器剪弯刚度,使设计工作更加高效。     

Buckling of circular, solid and annular plates with an intermediate circular support

The title problem is solved in the case where uniform applied loading is present at the plate outer boundary. Two independent solutions are obtained: the optimized Rayleigh–Ritz method and the finite element algorithmic procedure. Good engineering agreement is shown to exist. The proposed analytical procedure is convenient from a designer's viewpoint. Admittedly exact analytical solutions can be found in terms of Bessel functions, the procedure being rather complex from an engineering viewpoint.     

A novel array of elliptic ring radiators

An array of elliptic ring radiators is proposed which generates a fan-type beam with controllable sidelobe levels. Such an array has applications in specialized acoustic systems such as sidescan sonars, sonars for fish finding and stock assessment, obstacle avoidance systems, and others. Two possible approaches to the design are presented. One approach utilizes a mapping which transforms a radiation pattern generated by a circular ring array to that of an elliptic ring array. This approach takes advantage of methodologies developed for the design of circular ring arrays. The other approach uses the concept of an equivalent linear array. This approach benefits from existing design techniques developed for linear arrays. It requires only simple matrix operations and does not involve any optimization. The design examples presented demonstrate that a fan-type beam with sidelobes suppressed to more than 40 dB in all possible directions is achievable     

Some additional results on vibrating, simply supported rectangular plates with free, rectangular cut-outs

The present study deals with numerical experiments performed using the doublesine Fourier expansion and the Ritz method to determine natural frequencies of vibration of simply supported rectangular plates with free rectangular holes parallel to the plate sides.The problem is of basic structural interest in naval and ocean engineering systems since holes are frequently practiced in plate-type structural elements to allow for the passage of ducts, elevators, etc…     

Elastic properties of spherically anisotropic piezoelectric composites

Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.     

Three-dimensional Lump-Mass formulation of a catenary riser with bending, torsion and irregular seabed interaction effect

A three-dimensional Lump-Mass formulation of a catenary riser, capable of handling irregular seabed interaction, with bending and torsional stiffness is presented in this paper. This formulation uses only three degrees of translational freedom and one independent torque variable for each computational node. The generality of the present formulation permits static and dynamic analyses of a wide range of offshore-related slender structure systems such as mooring cables, rigid and flexible risers as well as submarine pipelines. Four sets of results are presented for (i) a hanging catenary, (ii) as (i) but subjected to end torsion, (iii) a wire, chain and spring buoy mooring and (iv) a steel catenary riser on an irregular seabed.     

Parametric study of geometrical effects on the degree of bending (DoB) in offshore tubular K-joints under out-of-plane bending loads

In this paper, results of comprehensive finite element (FE) analyses carried out on 81 generated models of tubular K-joints are presented. Results of FE models were verified against experimental data and parametric equations. The fatigue life of a tubular joint, which is commonly found in offshore industry, is not only dependent on the value of hot-spot stress (HSS), but is also significantly influenced by the through-the-thickness stress distribution characterized by the degree of bending (DoB). Data extracted from FE analyses was used to study the effects of geometrical parameters on the DoB values in tubular K-joints subjected to two types of out-of-plane bending (OPB) moment loads. The determination of DoB values in a tubular joint is essential for improving the accuracy of fatigue life estimation using the stress-life (S–N) method and particularly for predicting the fatigue crack growth based on the fracture mechanics (FM) approach. Geometrically parametric investigation was followed by a set of nonlinear regression analyses to develop DoB parametric formulas for the fatigue analysis of K-joints under OPB loadings.     

A unified, polynomial approach for the approximate solution of thermoelastic problems in rectangular plates

The present paper, of a tutorial nature, solves two different thermoelastic problems using a unified approach: (a) thermoelastic stresses and deflections in thin, rectangular plates with edges elastically restrained against rotation when small-deflection theory is used and stress resultants in the middle plane of the plates are neglected; and (b) thermoelastic plane stress situations in rectangular plates with stress-free edges subjected to a two-dimensional temperature distribution.The first problem is attacked using polynomial coordinate functions which identically satisfy the governing boundary conditions, and the Ritz method is used to determine the plate response. When the flexibility coefficients approach zero (clamped edge conditions) the calculated results practically coincide with the exact solution for the test case treated in this paper. On the other hand this degenerate solution turns out to be a very convenient approximation for obtaining a solution to Airy's problem described in the second place and which is also solved in a straightforward manner using a variational approach.     

套管加强T型管节点在平面外弯矩作用下极限强度分析

对用套管加强的T型管节点在平面外弯矩作用下的极限强度作了参数化分析。同时将相应的套管以及管节点的几何参数对极限强度的影响进行评估,并且和未加强的T型管节点作了比较。在计算结果中可以得出在管节点的弦管和撑管的连接处用合适的套管加强,可以将管节点在平面外弯矩作用下的极限强度提高到3倍多。