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Toroidal shells are widely used in structural engineering. The governing equations of toroidal shells are very complicated because of its variable coefficients with singularity. To find their analytical solution, traditionally, the complex form governing equations were proposed and some useful solutions were obtained. Unfortunately, no any closed-form solution has even been obtained for either general or slender toroidal shells. This paper focus on a special case of toroidal shells, i.e., slender symmetrical toroidal shells. For the first time, the closed-form solution of this kind of shell has been successfully obtained from displacement form governing equations. The closed-form solution is demonstrated for the example of thermal compensation devices. The correction of well-known Dahl formula for slender toroidal shell has been proposed based on the solution obtained in this paper. DOI: 10.1061/(ASCE)EM.1943-7889.0000175 CE Database subject headings: Shells; Axisymmetry; Bending; Deformation; Elasticity; Closed form solutions. Author keywords: Toroidal shells; Axisymmetry; Revolution shells; Slender shells; Bending; Deformation; Elastic materials.

This paper describes the interval boundary element method treatment of the pointwise discretization error for systems with geometrically generated flux singularities. Worst-case interval bounds are provided for the local discretization error for all elements except for the element with a singular flux solution, for which the flux intensity factor is enclosed. An example is presented showing the behavior of the interval bounds on the local discretization error for systems with geometrically induced singularities. DOI: 10.1061/(ASCE)EM. 1943-7889.0000109 CE Database subject headings: Boundary element method; Errors. Author keywords: Boundary element method; Interval boundary element method; Discretization error; Flux singularity; Flux intensity factor; Discretization error bounds; Flux intensity factor bounds.

Usually in the study of singularity problems, only the most critical singular order is considered. For three-dimensional interface corner problems, if only the most critical singular order of stresses is considered, it is possible to lose the opportunity to compute the full modes of stress intensity factors. To fully understand the failure behavior of three-dimensional interface corners, a definition of the stress intensity factors for the lower singular orders is proposed in this paper based on that of the most critical singular order. Moreover, to compute the proposed multi-order stress intensity factors accurately and efficiently, a path-independent H-integral, which has been proven useful for the two-dimensional interface corners, is now modified into a domain-independent H-integral for the three-dimensional interface corner problems. Because the stress intensity factors characterize the fracture behavior focused on an arbitrary tip along the corner front, based on anisotropic elasticity the near tip solutions and complementary solutions of two-dimensional generalized plane strain problems are introduced and then utilized for computation of three-dimensional H-integral. To illustrate the validity of the present work, several three-dimensional numerical examples are analyzed and compared with the existing published solutions. Finally, two examples about the interface corners, which occur frequently in electric packages, are solved to show the feasibility and practicability of the proposed approach. [DOI: 10.1115/1.4000411] Keywords: stress intensity factors, three-dimensional interface corner, domain-independent H-integral

The particular solutions of a two-dimensional infinite wedge for various boundary conditions with lnr weak singularity have been investigated in this paper. The relations of the weak singularities and the discontinuities of the first kind of the boundary variables at a corner of a two-dimensional elastic body have been established. By using the relations, the singular behaviors of the unknown boundary variables at a corner of an elastic body can be obtained before solving the boundary value problem by using the boundary element method (BEM). Especially, if the boundary conditions at a corner are displacements prescribed, the values of the unknown tractions at the corner can be determined in advance. Thus, the difficulty related to the multivalued tractions at a corner in BEM analysis for problems with boundary, displacements prescribed has been overcome completely. In addition, more appropriate shape functions for the unknown boundary field variables of a corner element can be constructed, and the accuracy of the BEM may be greatly increased. [DOI: 10.1115/1.3168599] Keywords: corner problem, boundary, displacement and traction, discontinuity of the first kind, weak singularity, boundary element method

By coupling the Donnell-Mushtari shell equations to an analytical inviscid fluid solution, the linear dynamics of a rotating cylindrical shell with a corotating axial fluid flow is studied. Previously discovered mathematical singularities in the flow solution are explained here by the physical phenomenon of blocking. From a reference frame moving with the traveling waves in the shell wall the flow is identical to the flow in a rigid varicose tube. When the ratio of rotation rate to flow velocity approaches a critical value, the phenomenon of blocking creates a stagnation region between the humps of the wall. Since the linear model cannot account for this phenomenon, the solution blows up. [DOI: 10.1115/1.2998486]

Generally, the mixed boundary value problems in fracture and contact mechanics may be formulated in terms of integral equations. Through a careful asymptotic analysis of the kernels and by separating nonintegrable singular parts, the unique features of the unknown functions can then be recovered. In mechanics and potential theory, a characteristic feature of these singular kernels is the Cauchy singularity. In the absence of other nonintegrable kernels, Cauchy kernel would give a square-root or conventional singularity. On the other hand, if the kernels contain, in addition to a Cauchy singularity, other nonintegrable singular terms, the application of the complex function theory would show that the solution has a non-square-root or unconventional singularity. In this article, some typical examples from crack and contact mechanics demonstrating unique applications of such integral equations will be described. After some remarks on three-dimensional singularities, the key examples considered will include the generalized Cauchy kernels, membrane and sliding contact mechanics, coupled crack-contact problems, and crack and contact problems in graded materials. [DOI: 10.1115/1.2936241]

The kinematic analysis and the determination of the singularity loci of spatial four-degree-of-freedom parallel manipulators with prismatic or revolute actuators are discussed in this article. A new method for the derivation of the velocity equations and the corresponding Jacobian matrices is presented. The numerical determination of the workspace boundaries is then briefly discussed. Finally, the determination of the singularity loci is performed using the velocity equations and examples are given to illustrate the results obtained. Spatial four-degree-of-freedom parallel manipulators can be used in several robotic applications as well as in flight simulators. The determination of their singularity loci is a very important design issue.

This paper is devoted to the description of the set of all singular configurations of serial robot-manipulators. For 6 degrees of freedom serial robot-manipulators we have developed a theory which allows to describe higher order singularities. By using Lie algebra properties of the screw space we give an algorithm, which determines the degree of a singularity from the knowledge of the actual configuration of axes of the robot-manipulator only. The local shape of the singular set in a neighbourhood of a singular configuration can be determined as well. We also solve the problem of escapement from a singular configuration. For serial robot-manipulators with the number of degrees of freedom different from six we show that up to certain exceptions singular configurations can be avoided by a small change of the motion of the end-effector. We also give an algorithm which allows to determine equations of the singular set for any serial robot-manipulator. We discuss some special cases and give examples of singular sets including PUMA 560.

The Eshelby-Stroh formalism for anisotropic elasticity is applied to evaluate stress singularities at grain triple junctions. The analysis defined different asymmetric grain boundary configurations and random orientations for both cubic and orthotropic grains. Both grain types showed super singularities for two-dimensional polycrystals in the fully symmetric case.

Characteristic equations are established to define stress singularity orders at the tip of a crack ending at an interface between two orthotropic media. Variations in alignment and angular relations to the interface are then examined for two general anisotropic materials. A general solution to the problem shows roots as gamma functions. Extension of the problem to include Krenk's parameters shows generalized Dundurs' constants as vital factors in analysis.

Arbitrary normal and shearing processes based on elasticity theory are applied to the three-phase bonded structure problem, which are defined by two interfaces and two free surfaces. Bonded wedge geometries displayed a direct relationship between material pairing and stress singularity order. Material bonding order also conditioned the singularity order for the given bonded structure.

In this paper we discuss singular configurations of serial robot-manipulators with respect to their removability. A removable singularity is a singularity which can be removed from a motion of the end-effector by a small change of the motion. The most interesting situation appears for robot-manipulators with 5 degrees of freedom, because the case of 4 degrees of freedom is easy and singular configurations of robot-manipulators with 6 degrees of freedom are nonremovable. In the paper we give the complete list of all 5R robot-manipulators which have nonremovable singularities. The image of the singular set in the parameter space for such manipulators can be a plane, a quadric, a cylinder or an algebraic surface of degree 3 or 7. All of them are explicitly given.

A geometric application of screw theory is used to develop a recursive algorithm for computing all singular configurations of revolute-jointed manipulators with arbitrary link geometries and an arbitrary number of joints. The depth of the recursion is linear in the number of joints, n, while the computational burden is proportional to [2.sup.n-2]. This method does not require explicit construction of the Jacobian matrix elements or a determinant operation. The method is also robust with respect to the bifurcations that occur for industrial robot geometries. Further, the screw axis of the singular motion is determined at no additional cost.

In this paper, the stability robustness of linear discrete-time singular systems with structured parameter perturbations is investigated. A new sufficient criterion is presented for ensuring that the linear discrete-time singular system remains regular, impulse-free, and asymptotically stable under structured parameter perturbations. The presented criterion is proved to be less conservative than the existing one reported recently.