Large Deformation Problem of Bimodular Functionally-Graded Thin Circular Plates Subjected to Transversely Uniformly-Distributed Load: Perturbation Solution without Small-Rotation-Angle Assumption

In this study, the large deformation problem of a functionally-graded thin circular plate subjected to transversely uniformly-distributed load and with different moduli in tension and compression (bimodular property) is theoretically analyzed, in which the small-rotation-angle assumption, commonly used in the classical Föppl–von Kármán equations of large deflection problems, is abandoned. First, based on the mechanical model on the neutral layer, the bimodular functionally-graded property of materials is modeled as two different exponential functions in the tensile and compressive zones. Thus, the governing equations of the large deformation problem are established and improved, in which the equation of equilibrium is derived without the common small-rotation-angle assumption. Taking the central deflection as a perturbation parameter, the perturbation method is used to solve the governing equations, thus the perturbation solutions of deflection and stress are obtained under different boundary constraints and the regression of the solution is satisfied. Results indicate that the perturbation solutions presented in this study have higher computational accuracy in comparison with the existing perturbation solutions with small-rotation-angle assumption. Specially, the computational accuracies of external load and yield stress are improved by 17.22% and 28.79% at most, respectively, by the numerical examples. In addition, the small-rotation-angle assumption has a great influence on the yield stress at the center of the bimodular functionally-graded circular plate.

Deformation Law and Control Measures of Gob-Side Entry Filled with Gangue in Deep Gobs: A Case Study

Aiming at the large deformation problem of gob-side entry in solid filling mining, the roof subsidence of gob-side entry retaining (GER) was studied under the influence of gangue filling, by taking a deep filling working face in Shandong Province as the engineering background and using theoretical derivation as well as FLAC3D numerical simulation. Research shows that the stiffness of the gangue filling body in the gob and the stiffness and width of the entry protection coal and rock mass (EPCARM) are positively correlated with the GER roof subsidence, which is much less affected by the EPCARM parameters than by the GER stiffness. The GER failure to meet the application requirements is mainly attributed to the insufficient stiffness of the gangue filling body and excessive advance subsidence, which inhibit the roof stress transfer. The GER replacement by the gob-side entry driving (GED) scheme, which implies replacing the entry protection gangue bag wall with the coal pillar with a width of 5 m, will reduce the roof subsidence to 0.114 m, according to the proposed equation. The results obtained are considered quite instrumental in deformation control of the gob-side entry filled with gangue, as well as substantiation of GED and GER applicability options.

Kinematic energy balance approach to submarine landslide evolution

The paper applies the energy balance kinematic method of plasticity theory to the large deformation problem of initiation and propagation of the spreading and ploughing failure outside a failed slab in submarine sediments. The models account for the phenomenon of the progressive propagation of a slope parallel slip surface, which is also quantified using the energy balance approach. In contrast to existing approximate analytical and numerical solutions, the proposed approach provides a theoretical basis for spreading and ploughing criteria as well as the comprehensive dynamic solution of the problem of post-failure landslide evolution. Incremental integration of the derived analytical expressions for kinetic energy in time allows for modelling recurrent initiation of new kinematic failure mechanisms with their subsequent large-scale deformation. Treating the failed slab as well as the spreading and ploughing mechanisms as one composite dynamically evolving mass movement allows for the final post-failure geomorphology of the failed slope to be predicted using basic mechanical principles.

Detailed Parametric Investigation and Optimization of a Composite Wing with High Aspect Ratio

The large deformation problem of the wing with high aspect ratio cannot be avoided due to the large bending moment and poor torsional stiffness. The wing design follows the following procedure; firstly, the design indexes of high aspect ratio wing are preliminarily formulated referring to some parameters of the Predator UAV. Then, the aerodynamic analysis of the wing is performed, and the stress cloud diagram is obtained. Next, the finite element model of the wing is designed, and the static analysis is conducted in the ANSYS ACP module, and the unreasonable component size is changed. An appropriate thickness which is 12 mm is selected as the final thickness of the wing. Then, the analysis of laying methods of skin structure is conducted. Finally, the composite structure is proved to reduce the maximum deformation and maximum stress effectively compared with the metal wing.

Nonlinear Large Deformation of Graphene Sheets Using a Nonlocal-Based ANCF Method

A novel nonlinear model of single-layered graphene sheets (SLGSs) subject to large deformation is proposed using the absolute nodal coordinate formulation (ANCF) and the nonlocal elasticity theory. The geometrical definition of SLGSs is described by ANCF thin plate element while the strain energy is expressed by nonlocal theory. Then, the formulation of elastic force and the Jacobian of the elastic force is derived. We verify the proposed model by comparing the results with other published results and conduct corresponding numerical case study to clarify the influence of boundary conditions (BCs), nonlocal parameters, side length and aspect ratio. Large deformation problem of SLGSs with several BCs and different loading modes are simulated to study the mechanical nonlinearity of the SLGSs.

Numerical simulation and analysis of the dynamic finite element model of the fiber motion in the air spinning process

Under the spinning technology of the air-assisted twisting, this paper established the fiber finite element model, which has the structural and dynamic characteristics of the fiber flexible body, based on the space elastic thin rod unit. In this research, we deduced the static equilibrium equation of the fiber finite element model. The nonlinear geometric displacement large deformation problem of the space elastic thin rod unit was treated by the method of stepwise loading successive approximation, and the finite element simulation and analysis of the fiber flexible body’s movement and deformation during the air-jet twisting were carried out and verified by experiment in this paper. This research presents an effective and feasible theoretical model and method for the flexible fiber twisting formation process and mechanism under the high velocity vortex airflow.

Study on the Centrifugal Atomization Process of Molten Slag with the Coupled Algorithm of Three-Dimensional SPH-FEM

The SPH method was introduced to simulate the centrifugal atomization process between molten slag and rotary disc since the traditional method based on grid cannot effectively solve the large deformation problem. Coupling the SPH method with FEM was realized through the coupled algorithm based on penalty function. The effectiveness of coupling algorithm used for calculating the centrifugal atomization process was affirmed. Under the condition that speed of rotary disc and molten slag flow are 1500rpm, 0.1m/s, respectively, the speed of molten slag particles that are directly colliding with the rotary disc is in a range from 2.5m/s to 3.0m/s as soon as that of molten slag particles disturbed by stress wave is in a range from 0.25m/s to 0.8m/s with the characteristics of volatility. This study is helpful for optimizing atomization process design and energy-saving efficiency.