Stress concentration around a part-through hole weakening a laminated plate

A quasi-three-dimensional-elasticity type theory, based on the assumptions of transverse inextensibility and layerwise constant shear-angle, is presented, in the context of an assumed quadratic displacement potential energy approach, for analyzing an edge-loaded laminated plate weakened by the presence of a part-through hole. Numerical results, obtained using the C°-type triangular finite element, indicate the existence of severe cross-sectional warping in the vicinity of the hole and plate boundaries. Furthermore, the three-dimensional nature of the stress concentration factor in the neighborhood of the hole boundary is clearly exhibited. Besides, very high stress concentration factors are found in the layer weakened by the part-through hole. The numerical results presented should serve as bench-mark solutions for future comparisons.     

A special boundary-element formulation for multiple-circular-hole problems in an infinite plate

A special boundary-element formulation is proposed to solve the multiple-circular-hole problems in an infinite plate. The main ideas of the proposed formulation are followed from two directions. The first formulation in which, all the unknowns are taken from the boundary tractions, is like the boundary-element method. In the second, all the derivations of the solution are derived from the complex variable method of plane elasticity. Using the principle of superposition, a system of linear algebraic equations for the unknowns is established. Finally, several numerical examples are given.     

Mixed legendre-hermite spectral method for heat transfer in an infinite plate

Nonisotropic heat transfer in an infinite plate is considered. A weak formulation is derived, which is appropriate for its numerical simulation. The mixed Legendre-Hermite spectral method is proposed for this problem. Its convergence is proved. Numerical results show the efficiency of this new approach.     

Modeling of transient bending wave in an infinite plate and its coupling to arbitrary shaped piezoelements

Estimating the location and energy of impacts is of primary importance for assessing the condition of structures. Particularly, such estimation can be easily obtained from the energy flow in the structures, which is usually derived from the Poynting vector. In order to measure the Poynting vector in a thin plate using piezoelements bonded on the plate, an analytical formulation of the impulse response in thin infinite plates is presented. The knowledge of the impulse response of any linear time invariant (LTI) system is precious information for the determination of its behavior under arbitrary inputs. When dealing with propagation, and especially mechanical wave propagation, a common approach consists in using numerical methods that are often time-consuming, especially for multi-coupled systems. This paper proposes a new approach for modeling the impulse response of an infinite plate with surface-bonded piezoelectric elements. The proposed analytical formulation allows bypassing numerical analysis drawbacks, in particular instabilities occurring at high frequencies, case-dependent systems and computational requirements, while giving the response for any time and space domain values using a simple convolution. The proposed model relies on flexural wave decomposition over the spatial frequency domain and corresponds to a time generalization of the angular spectrum theory, thus introducing flexural wave propagation as a time-varying spatial filter. Once the impulse is know in the spatial frequency domain, the inverse Fourier transform is applied and leads to the impulse response in the physical domain. From this model, an analytical expression of the impulse voltage response of the piezoelectric transducers and the Poynting vector can be derived quite easily. The predicted impulse response is then compared to FEM simulation results and experimental measurements in order to assess the model.     

Effective stiffness and microscopic deformation of an orthotropic plate containing arbitrary holes

Many engineering materials and structures, such as cellular structures, sandwich core structures and laminated plates with holes, can be modeled by an inclusion problem with anisotropic matrix. The paper studies the effective properties and the microscopic deformation of anisotropic plates with periodic holes by using direct and mathematical homogenization. The effective stiffnesses are calculated by different homogenization methods and the microscopic deformation of a RVE is modeled by the finite element method for the plate with arbitrarily shaped holes. All of the effective stiffness coefficients, especially stretching-shear coupling coefficients are evaluated.     

Topological sensitivity derivative with respect to area,shape and orientation of an elliptic hole in a plate

The topological sensitivity derivative of a functional expressed in terms of displacement, strain or stress fields and boundary tractions is derived for the case of an elliptical hole introduced in the plate. The derivative is specified with respect to the hole area, the length of ellipse axes and their orientation in terms of primary and adjoint state fields. The shape sensitivity derivative for a finite hole can be applied and the topological derivative with respect to the hole area is obtained in the limiting case. The transition to a plane crack occurs for vanishing length of minor axis and the topological derivative with respect to crack length is then derived from the general formulae. The results can be useful in optimal design procedures by selecting positions, shape and orientation of elliptical cutouts.     

Interlaminar stress analysis for laminated plates containing a curvilinear hole

This study presents a variational-perturbation approach for the three-dimensional stress analysis around a curvilinear cutout in composite laminates. The solution is based on a composite expansion and assumed stress finite element methods. Stress field solutions for angleply and cross-ply laminates containing an elliptical hole have been presented. The effects of the ellipse aspect ratio and the fiber orientation on the interlaminar shear stress magnitude have been investigated. A failure criterion based on the interlaminar distortional energy function has been suggested. According to this criterion, it was found that, for angle-ply laminates containing an elliptical hole, a delamination failure initiation occurs at a point along the perpendicular to the direction of loading.     

Control of an amplifying wave on an infinite continuum

Previous work on the space-sampled feedback control of continuum instabilities in flowing systems is extended. When the continuum over which control is desired is many wavelengths long, it is often convenient to construct the control system of many sampling stations, each approximately one wavelength in size. The stability of such a system is discussed, and a new type of instability is found which does not appear when the system is small in terms of a wavelength.     

飞机腐蚀搭接板的应力分析

为降低由于铝合金腐蚀产生的膨胀作用引起的枕垫效应对飞机搭接板应力的影响,利用非线性有限元法分别对不同铆钉弹性模量、不同搭接板弹性模量和不同搭接板泊松比下的腐蚀搭接板进行仿真分析.结果表明：枕垫效应对搭接板应力的影响随着铆钉弹性模量的增大、搭接板弹性模量和泊松比的减小而减小.     

Extending Hoare Logic with an Infinite While-Rule

In the paper we generalize the while-rule in Hoare calculus to an infinite one and then present a sufficient condition much weaker than the expressiveness for Cook‘2 relative completeness theorem with respect to our new axiomatic system.Using the extended Hoare calculus we can derive true Hoare formulas which contain while statements free of loop invariants.It is also pointed out that the weak condition is a first order property and therefore provides a possible approach to the characterization of relative completeness which is also a first order property.     

Optimal hole shape for minimum stress concentration using parameterized geometry models

The goal of this work is to obtain optimal hole shape for minimum stress concentration in two-dimensional finite plates using parameterized geometry models. The boundary shape for a hole is described by two families of smooth curves: one is a “generalized circular” function with powers as two parameters; the other one is a “generalized elliptic” function a and b are ellipse axes) with powers as two parameters and one of the ellipse axes as the third parameter. Special attention is devoted to the practicability of parameterized equations and the corresponding optimal results under the condition with and without the curvature radius constraint. A number of cases were examined to test the effectiveness of the parameterized equations. The numerical examples show that extremely good results can be obtained under the conditions with and without curvature radius constraint, as compared to the known solutions in the literature. The geometries of the optimized holes are presented in a form of compact parametric functions, which are suitable for use and test by designers. It is anticipated that the implementation of the suggested parameterized equations would lead to considerable improvements in optimizing hole shape with high quality.     

Analysis of an infinite multi-server queue with an optional service

This paper deals with an infinite-capacity multi-server queueing system with a second optional service (SOS) channel. The inter-arrival times of arriving customers, the service times of the first essential service (FES) and the SOS channel are all exponentially distributed. A customer may leave the system after the FES channel with a probability (1 − θ), or the completion of the FES may immediately require a SOS with a probability θ (0 ? θ ? 1). The formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is developed to simultaneously determine the optimal values of the number of servers and the two service rates at the minimal total expected cost per unit time. Quasi-Newton method and Particle Swarm Optimization (PSO) method are employed to deal with the optimization problem. Under optimal operating conditions, numerical results are provided from which several system performance measures are calculated based on the assumed numerical values of the system parameters.     

Stress analysis of an elastic plate with an opening or notches under tension based on the concept of general systems

The paper presents a method of calculation dealing with plane stress problems, based on the concept of general systems theory. The first part makes a proposal for calculating the stresses and the stress concentration factor of an elastic plate with a circular hole under tension. The remainder describes its application to similar problems, such as an elastic plate with an elliptical hole, an oval hole and semi-circular notches under tension. The stresses at any point in a plate are calculated from the effect of the stresses on the boundaries. General systems theory suggests state object evolves at discrete times. The deformation of the plate is supposed to take a few steps along the time axis, though the real deformation finishes at one step. The results were compared with analytical solutions and/or experimental results.     

Triangular element for analysis of a stretched plate weakened by a part-through hole

A C⁰-type triangular element formulation in orthogonal curvilinear coordinates has been developed, based on assumptions of transverse inextensibility and layerwise constant shear angle for analysis of a stretched homogeneous plate weakened by a part-through hole. The element stiffness matrix and consistent load vector have been derived using assumed quadratic displacement (in curvilinear coordinate plane) potential energy approach. Numerical results obtained using the straight-sided triangular element version indicate the presence of transverse shear deformation in a stretched homogeneous plate weakened by a symmetrically located concentric hole     

A finite and an infinite Whittaker integral transform

This paper is concerned with the construction and study of specific finite and infinite integral transforms arising from a singular Sturm-Liouville problem on a half line, which is connected to the hydrogen atom equation. The paper goes further to describe fully the image of some spaces of square integrable functions with respect to some measure under the finite and infinite integral transforms.     

Heat and mass transfer phenomena in the flow of Casson fluid over an infinite oscillating plate in the presence of first-order chemical reaction and slip effect

The objective of this article is to study the physics of slip effect at the boundary of a vertical plate in starting the flow of Casson fluid with the combined effect of radiative heat and mass transfer in the presence of first-order chemical reaction. The problem has been modeled in terms of partial differential equations along with appropriate initial and boundary conditions. The dimensionless governing equations have been solved by means of the Laplace transform technique. Exact solutions have been obtained for velocity, temperature and concentration profiles. The obtained velocity has been computed in tabular form for steady and transient velocities. The physics of velocity profile has been studied for various physical parameters through numerical computation and displayed in graphs. From obtained solutions, the well-known published results in the open literature have been recovered and displayed in graphs and tables.

     

Asymptotic stability and discretization on an infinite interval

By imposing some conditions on the discrete dynamical systems generated by one step discretization methods, we construct some non linear one step methods of the first and second order, which turn out to beA-stable orL-stable according to the current definitions. Numerical experiments are carried out on some common stiff test problems, confirming the validity of the methods.     

Verifying an infinite systolic algorithm using third-order equational methods

We consider using third-order equational methods to formally verify that an infinite systolic algorithm correctly implements a family of convolution functions. The detailed case study we present illustrates the use of third-order algebra as a formal framework for developing families of computing systems. It also provides an interesting insight into the use of infinite algorithms as a means of verifying a family of finite algorithms. We consider using purely equational reasoning in our verification proofs and in particular, using the rule of free variable induction. We conclude by considering how our verification proofs can be automated using rewriting techniques.