Solving the hourglass instability problem using rare mesh variation-difference schemes

The hourglass instability effect is characteristic of the Wilkins explicit difference scheme or similar schemes based on two-dimensional 4-node or three-dimensional 8-node finite elements with one integration point in the element. The hourglass effect is absent in schemes with cells in the form of simplexes (triangles in two-dimensional case, tetrahedrons in three-dimensional case). But they have another well-known drawback - slow convergence. One of the authors proposed a rare mesh scheme, in which elements in the form of a tetrahedron are located one at a time in the centers of the cells of a hexahedral grid. This scheme showed the absence “hourglass” effect and other drawbacks with high efficiency. This approach was further developed for solving 2D and 3D problems.

Study on Dynamic Response Characteristics and Damage Mechanism of Tunnel Lining at Entrance of Shallow Bias Tunnel

The structural damage of the lining structure at the entrance of a tunnel is the most common instability problem. The instability problem may cause dynamic effects such as earthquakes and blasting. Based on the seismic damage data collected from previous major earthquakes at the entrance of shallow-buried tunnel, the shaking table test and numerical simulation are used to analyze dynamic response characteristics and damage evolution characteristics of the tunnel in the shallow-buried hole at 30°. The study revealed the stress characteristics of tunnel lining and the mechanism of structural damage under earthquake excitation. The research results show that the biased tunnel (30°) is susceptible to damage on the unsymmetrical loading side, the biased ground surface leads to acceleration, and high speed also significantly increases the effect. The biased side leg of the tunnel lining cross section is a location with a large internal force distribution. The biased tunnel has a relatively unfavorable internal force value distribution and a larger peak, and the peak at the larger bias side has the largest peak value. The skewback and spandrel portion of the biased tunnel lining load are more likely to be damaged.

Application of Geomechanics for Successful Drilling of Onshore Well with Multiple Challenges of Losses and Intense Gas Cut Mud in Naturally Fractured Zone.

Drilling of deviated development wells in O-field X has proven to be challenging. Drilling experience in several wells within the field has different issues of wellbore instability, most recent is when traversed through a pre-existing/naturally fractured intervals. Numerous lost-time incidents related to wellbore instability-related problems were experienced, ranging from tight hole (remedied by reaming) to Overpulls, pack-off followed by stuck pipe, fill on-bottom to difficulties in running casing, and tensile cavings to high gas associated with drilling breaks. These problems were observed particularly when drilling previous and current wells in the O-field X. Many of the wells in O-field X were drilled with water-based mud (WBM) for top-hole and POBM for intermediate hole section. However, drilling the most recent well became more challenging with issues of severe losses just below the 13-3/8inch shoe where an interbedded lignite formation characterized with pre-existing fractures was drilled through. Faced with continual non-productive time (NPT), the predrill GeoMechanical report was immediately reviewed coupled with the stress caging procedure adopted to further mitigate the loss circulation wellbore instability problem. The recommendations arising from the comprehensive review of the GeoMechanical window, stress caging and drilling experience analyses was immediately implemented to improve performance which has helped in drilling the well to final completion. This paper highlights the importance of integrating GeoMechanics, stress caging and with proper drilling practices which has helped in delivery of the candidate well. A full-scale GeoMechanical window review was proactively adopted considering the mid-line collapse gradient approach for unconsolidated, naturally fracture formations and critical depleted intervals. All the above strategies were adopted, which assisted in safe delivery of candidate well in O-field X.

BUCKLING DELAMINATION IN COMPRESSED NO-TENSION HOMOGENEOUS BRITTLE BEAM-COLUMNS REINFORCED WITH FRP

The main issue of this paper is the instability of no-tension structural members reinforced with FRP. This study concerns the instability of FRP reinforcement. The primary instability problem of a compressed element involves the partialization of the inflex section. In particular, in the case of a compressed slender element reinforced on both tense and compressed side FRP delamination phaenomenon could occur on the latter. This entails the loss of the reinforcement effectiveness in the compressed area for nominal load values much lower than material effective strength. Therefore, structural elements or portions thereof which absorb axial components in the direction of the reinforcement may exhibit relatively modest performance with respect to the unreinforced configuration. By employing a no-tension material linear in compression, an analytical solution for FRP buckling delamination length is provided. The main objective of this paper is to provide a simplified tool that allows to evaluate the critical load of the reinforced beam-column and to predict the tension at which delamination and the loss of effectiveness of reinforcement in the compressed area could occur.

Emergent universe and Genesis from the DHOST cosmology

In this article, we present an emergent universe scenario that can be derived from DHOST cosmology. The universe starts asymptotically Minkowski in the far past just like the regular Galileon Genesis, but evolves to a radiation dominated period at the late stage, and therefore, the universe has a graceful exit which is absent in the regular Galileon Genesis. We analyze the behavior of cosmological perturbations and show that both the scalar and tensor modes are free from the gradient instability problem. We further analyze the primordial scalar spectrum generated in various situations and discuss whether a scale invariance can be achieved.

A Nonlinear Analysis of the Wahl–Fischer Torsional Instability

This is an extension to a previous study of the Wahl–Fischer torsional instability problem (Infante and Doughty, “An Old Problem Reconsidered: The Wahl–Fischer Torsional Instability Problem”, J. Appl. Mech. Trans. ASME, 2020, 87(10), p. 101004). There, we provided a mathematical explanation of the reasons for the existence of torsional oscillations observed in numerical simulations and in actual mechanical devices such as the exhaust fan system studied by Wahl and Fischer. That explanation was mostly based on linear analysis. This paper presents an additional mathematical explanation of the nature and form of the large self-excited oscillations, due to the strongly nonlinear nature of the system and the large amplitude of these oscillations. Because the oscillations are large, their study requires the use of nonlinear methods.

Error analysis of higher order trace finite element methods for the surface Stokes equation

The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in ℝ3. The method employs parametric Pk-Pk−1 finite element pairs on tetrahedral bulk mesh to discretize the Stokes system on embedded surface. Stability and optimal order convergence results are proved. The proofs include a complete quantification of geometric errors stemming from approximate parametric representation of the surface. Numerical experiments include formal convergence studies and an example of the Kelvin--Helmholtz instability problem on the unit sphere.

Accurate Computation of Fractional-Order Exponential Moments

Exponential moments (EMs) are important radial orthogonal moments, which have good image description ability and have less information redundancy compared with other orthogonal moments. Therefore, it has been used in various fields of image processing in recent years. However, EMs can only take integer order, which limits their reconstruction and antinoising attack performances. The promotion of fractional-order exponential moments (FrEMs) effectively alleviates the numerical instability problem of EMs; however, the numerical integration errors generated by the traditional calculation methods of FrEMs still affect the accuracy of FrEMs. Therefore, the Gaussian numerical integration (GNI) is used in this paper to propose an accurate calculation method of FrEMs, which effectively alleviates the numerical integration error. Extensive experiments are carried out in this paper to prove that the GNI method can significantly improve the performance of FrEMs in many aspects.

An Old Problem Reconsidered: The Wahl–Fischer Torsional Instability Problem

The phenomenon of torsional instabilities found in rotating mechanical systems powered by induction motors was encountered in the late 1930s by Wahl and Fisher in a turnpike exhaust system. Subsequently, this phenomenon has been repeatedly found to affect a number of similar physical systems and has led to a number of studies and analysis that have clarified the reasons for these instabilities, associated with the torque characteristics of induction motors. Surprisingly, none of these studies have presented a mathematical qualitative analysis of the eigenvalues of the differential equations that describe such electromechanical systems. This is the central purpose of this paper. It depends on the identification and exploitation of a particular “central” solution to the differential equations that describe the system, and of its relationship to a simpler formulation of the same system. This turns out to be a rather modest mathematical endeavor which, however, yields result that illuminate the nature of the instabilities encountered and provides a designer of such systems with the tools to abate or avoid these instabilities.

Novel Spherical Polymer Sealing Agent for Oil-Based Drilling Fluids to Overcome Borehole Instability Problem in Low Permeability Reservoirs

Due to borehole instability problem in low permeability formations, a new type of spherical polymer sealing agent (OLBS) for oil-based drilling fluids was prepared via suspension polymerization, and the sealing effect of polymer sealing agent on low permeability cores was evaluated. The results indicated that OLBS had no influence on the rheological properties of oil-based drilling fluids. The core displacement experiments indicated that OLBS could reduce the core permeability by a significant amount, and thus stop fluid invasion into the formations, so OLBS could provide an excellent sealing effect and improve wellbore strength. Using this polymer sealing agent to plug the low permeability formations is a very powerful approach to address borehole instability problem in troublesome low permeability formations. This sealing agent is suitable for the drilling of long sections of horizontal laterals. In the future, the oil-based drilling fluids containing OLBS might hold great promise to resolve borehole instability problem in low permeability formations.