In order to design a tubular joint to carry a larger load and to possess a longer life, the prime objective of design would be to reduce stress concentration factor at the intersection of the joint; one method to achieve the same is to stiffen the joint with internal ring stiffeners. This paper presents results of the stress analysis for stress distribution, along the intersection of internally ring-stiffened tubular T-joints, under the action of axial and in-plane/out-of-plane (bending) loads, using degenerate shell elements. The stress analyses results are obtained using the general-purpose finite element package called ABAQUS. Post-processing of results has been facilitated by other small programs developed for the purpose. The nominal brace stress and the maximum principal stress values have been used for stress concentration factor computations. The effects of stiffener size, location, number, thickness (τ) and thinness (γ) ratios have been investigated, and the results validated with known analytical and experimental investigations. A comparison of the results obtained from finite element analysis, and experimental results of the Canadian Cooperative Fatigue Studies Program, carried out at Memorial University and University of Waterloo, is also made. The results obtained indicate that stiffening can considerably reduce the stress concentration in joints, and thus increase the load-carrying capacity of tubular T-joints.
A B S T R A C T Dynamic crack propagation in non-plane strain (or 3D) slate blocks under wedge impact loads was investigated numerically in this part of the paper. A parabolic-shaped crack trajectory was taken into consideration to model the crack propagation in slate blocks for analyzing the impact splitting of layered slate rock. Major and minor axes of the parabola were determined from the condition of equal mode I stress intensity factors (SIFs) along the crack front. Mode I SIFs were determined for experimental breaking loads for each increment of crack growth in a manner similar to that mentioned in part I of this paper. These values were compared with the plane strain material fracture toughness value obtained from experimental studies and very good agreement was obtained between them, for the case of actual load applied on the specimen. Numerical analysis of a field problem, i.e., separation of a large-sized slate slab from the rock strata in a slate quarry using wedge impacting, was also carried out in this paper. It can be observed that a large magnitude of load is required to break large-sized slate blocks; but this load is applied through a number of smaller load-capacity actuators-in-parallel, requiring large power capacity for the hydraulic pumps. However, this required power could be reduced considerably if the load applied on the line of hydraulic actuators is cascaded across the (line of) actuators (starting from centrally placed actuators) with a small time delay (equal to the initial crushing time in slate rock).These studies were motivated by the need to estimate theoretically the required in-plane impact loads for splitting layered slate rocks; in addition, the design of the necessary machinery/equipment to apply that load was also required in this study. The experimental testing of large-scale specimens will generally be beyond the reach of a researcher working in a medium-sized research laboratory. The other way to do the same is to verify and establish a numerical methodology from the results of small-scale experimental investigations and then to apply the same numerical procedure to compute the approximate breaking loads for large-sized slate blocks. From these computed breaking loads, the field equipment can be designed and fabricated.Two-dimensional and their equivalent plane strain (3D) finite-element analyses of the dynamic crack propagation of slate blocks, broken experimentally under plane strain conditions (transverse length of the block was equal to the transverse length of the wedge), were reported in part I of this paper. However, the prevalence of plane strain conditions for a rock breaking process is rather a rare event. Generally the loading area, or the extent of line load, would be much smaller than the length of the slate rock over which the failure of slate block is to be initiated. This leads to a 3D loading condition. Therefore, it is necessary to analyze large-sized slate blocks numerically as well. In part II of this paper, laboratory test results, and numerical analy...
SUMMARYThe present study concerns the analysis of bending of plates and shells subjected to various boundary conditions and load. Bending stress intensity factors for plates containing through-thickness crack under edge bending load are evaluated. To accomplish this task, hierarchical degenerated plate/shell and crack-tip singular plate/shell elements were developed.The hierarchical degenerated plate shell element has four corner nodes, four mid-side nodes and one central node on the mid-surface of the shell geometry with five degrees of freedom at each node. p-Version shape functions up to order seven were used for defining the displacement field. Enriching the displacement field with the asymptotic displacement field near the crack tip, a crack-tip singular plate/shell element was developed. Some benchmark problems were analyzed and compared. Analyses were performed to obtain the stress intensity factors of plate with through-thickness crack using singular hierarchical degenerated plate/shell element around the crack tip. Numerical results obtained from the present element formulations are compared with analytical/numerical solutions available from literature. It is inferred that numerical results are in good agreement with the benchmark plate and shell problems.
In this paper the dynamic response of a skew bridge deck has been investigated, treating it as an orthotropic plate and using the finite strip method. Employing the normal mode method, the response of the deck due to a moving force has been calculated. Williams' method has been used to accelerate the convergence of the solution. Numerical work has been done for different skew angles and speed ranges. In this study, the history curves and the maximum amplification spectra for deflection and bending moment are presented.
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