International Journal of Computational Methods

In this study, element-free Galerkin method (EFGM), a meshless method, is proposed for wrinkling analysis of pre-stressed rectangular membranes. The mathematical model for studying wrinkling of pre-stressed membranes is derived by considering the bending stiffness, though it is negligible. Moving least-square approximation for deflection is constructed by considering three degrees of freedom per node. Essential boundary conditions are imposed using scaled transformation matrix method. Initially, compression-induced buckling of a homogeneous thin plate without pre-stress is solved to validate the method and then a pre-stressed homogeneous membrane is analyzed for both compression-induced and shear-induced wrinkling. Capabilities of the proposed method for membrane analysis are compared with that of the finite element method (FEM). Comparative study on wrinkling analysis using EFGM and different FEM element types in a commercial FEM package shows that in lower modes both methods show satisfying consistency in eigenvalues with respect to the total of number of nodes, while at higher modes EFGM shows better consistency than FEM. Further, the study is extended to wrinkling of nonhomogeneous membranes subjected to linearly-varying in-plane load. The results obtained from EFGM analysis is compared and found to be matching well with those available in the literature.

To improve the accuracy of the standard finite element (FE) solutions for acoustic radiation computation, this work presents the coupling of a radial point interpolation method (RPIM) with the standard FEM based on triangular (T3) mesh to give a coupled “FE-Meshfree” Trig3-RPIM element for two-dimensional acoustic radiation problems. In this coupled Trig3-RPIM element, the local approximation (LA) is represented by the polynomial-radial basis functions and the partition of unity (PU) concept is satisfied using the standard FEM shape functions. Incorporating the present coupled Trig3-RPIM element with the appropriate non-reflecting boundary condition, the two-dimensional acoustic radiation problems in exterior unbounded domain can be successfully solved. The numerical results demonstrate that the present coupled Trig3-RPIM have significant superiorities over the standard FEM and can be regarded as a competitive numerical techniques for exterior acoustic computation.

This work presents a data-driven approach for the automated risk estimation of the voyage of a vessel or ship. While the industry is moving from a compliance-based framework with existing rules to a risk-based one, there is also a need to monitor the risk of a vessel from the perspective of the navigation. This is of even higher importance for the case of autonomous ships. Built based on the state-of-the-art mathematical representation, the navigation feature, each existing voyage is transformed into a corresponding series of points in $d$-dimensional space. During the stage of pre-processing, given a set of historical Automatic Identification System (AIS) data, those records that belong to the same vessel within a certain period of time are taken as a voyage and mapped to the corresponding space of the navigation feature. After the pre-processing and during the online monitoring, the current trajectory of the vessel is transformed into the corresponding representation in the same way. Based on a nearest-neighbor search scheme, the distance from the nearest neighbor is taken as the risk of the current voyage. In other words, the deviation from the closest route in the historical data is taken as the risk. The developed method has demonstrated encouraging performance on a set of challenging historical AIS data from the Australian Maritime Safety Authority, covering three regions in the Australian territory, namely, the Bass Strait, the Great Australian Bight and the North West.

The paper presents examples of approximate calculations of force values in members of selected types of trusses, which are at the same time an internal and external statically indeterminate systems. The two-stage method makes possible the approximate calculation of such trusses by help of, for example, the Cremona’s method. In each stage, a statically determinate truss is considered, pattern of which is defined by removing from the basic truss a suitable number of members. There are also presented results of calculations of the same trusses done by means of suitable computer software together with analyses and comparison of outcomes.

Computer aided design (CAD) models are widely employed in the current computer aided engineering or finite element analysis (FEA) systems that necessitate an optimal meshing as a function of their geometry. To this effect, the sub-mapping method is advantageous, as it segments the CAD model into different sub-parts, with the aim mesh them independently. Many of the existing 3D shape segmentation methods in literature are not suited to CAD models. Therefore, we propose a novel approach for the segmentation of CAD models by harnessing deep learning technologies. First, we refined the model and extracted local geometric features from its shape. Subsequently, we devised a convolutional neural network (CNN)-inspired neural network trained with a custom dataset. Experimental results demonstrate the robustness of our approach and its potential to adapt to augmented datasets in future.

Matched interface and boundary (MIB) method is introduced for free vibration analysis of irregular membranes. Two distinct schemes-on-interface and off-interface schemes are used to deal with the topological relations between edges of irregular domains and the Cartesian mesh lines. Different geometric shapes such as triangle and quadrilateral are dealt with by using MIB procedures. A number of examples are chosen to demonstrate the accuracy and convergence of MIB method. Numerical results show that MIB method is an efficient and highly accurate approach to solve free vibration problems of irregular membranes. This study further extends the application of MIB.

In this paper, an adaptive phase-field scaled boundary finite element method for fracture in functionally graded material (FGM) is presented. The model accounts for spatial variation in the material and fracture properties. The quadtree decomposition is adopted for refinement, and the refinement is based on an error indicator evaluated directly from the solutions of the scaled boundary finite element method. This combination makes it a suitable choice to study fracture using the phase field method, as it reduces the mesh burden. A few standard benchmark numerical examples are solved to demonstrate the improvement in computational efficiency in terms of the number of degrees of freedom.

Setting friction pendulum bearings (FPB) at the top of central columns may be a good strategy to reduce the stations’ seismic responses. In this paper, the FPB is simulated in a detailed manner. The seismic reduction effectiveness of the FPB is studied with the three-dimensional dynamic time history analysis method. It is found that FPB can effectively reduce the maximum shearing force of the central columns and slightly reduce the maximum bending moment. It is stated that FPBs are also effective in the underground station structures.

This paper aims to noninvasively estimate the sizes and locations of tumors via the surface temperature in the skin tissue. The famous 2D Pennes bioheat transfer equation is used to describe the heat transfer behavior in the skin tissue, which is solved by the recently-developed meshless generalized finite difference method (GFDM) in the proposed solver. The hybrid optimization algorithm based on genetic algorithm (GA) and Levenberg–Marquardt algorithm (LM) is introduced to estimate the sizes and locations of tumors. The efficiency of the proposed GA–LM–GFDM solver is verified under several benchmark examples. Numerical investigation shows that the tumor characteristics can still be accurately estimated with the contaminated temperature data measured on the skin surface.

This research was conducted to develop the three-dimensional (3D) finite element model of human skin for bio-heat transfer analysis. The skin burn was analyzed using Penne’s bio-heat equation, which has been adopted in many commercial finite element software. Burn injuries mostly occur due to heat transfer from hot object, hot liquids, cooking flames, and sometimes due to exposure to chemicals, electricity, and ionizing radiation. Depending upon the condition and duration of exposing, thermal burn may cause severe skin damage. The burn effect on human skin under the contact with a hot object or hot fluid was analyzed in this paper. The burn intensity in terms of degrees of burn was measured with different burning conditions and their corresponding time was graphically shown. Using the temperature profile obtained from the analysis, various methods of burn treatment were evaluated and compared. The results from this analysis will help to understand human skin burn under different burning conditions and treatment of different burn injuries.

This work is about a heat transfer phenomenon in relation to the periodically laminated composite. The specific type of thermal loading, analyzed in this paper, require formulation of Robin boundary conditions. To consider a layered structure of analyzed composite, the tolerance averaging technique is used. This method allows to take into account a thickness of the layers and obtain the equations with continuous coefficients. To solve these equations, the finite difference method is used, because an analytical solution is not available in this case (in contrast to the analogous issue in relation to a homogeneous layer).

Identifying centers of vortices of fluid flow accurately is one of the accuracy measures for computational methods. After verifying the accuracy of the 2D adaptive mesh refinement (AMR) method in the benchmarks of 2D lid-driven cavity flow, this paper shows the accuracy verification by the benchmarks of 2D backward-facing step flow. The AMR method refines a mesh using the numerical solution of the Navier–Stokes equations computed on the mesh by an open source software Navier2D which implemented a vertex centered finite volume method (FVM) using the median dual mesh to form control volumes about each vertex. The accuracy is shown by the comparison between vortex center locations calculated from the linearly interpolated numerical solutions and those obtained in the benchmark. The AMR method is proposed based on the qualitative theory of differential equations, and it can be applied to refine a mesh as many times as required and used to seek accurate numerical solutions of the mathematical models including the continuity equation for incompressible fluid or steady-state compressible flow with low computational cost.

This paper presents an efficient numerical technique capable of handling the stress analysis of three-dimensional cracked bodies strengthened by adhesively bonded patches. The proposed technique is implemented within the framework of the coupling of the weakly singular boundary integral equation method and the standard finite element procedure. The former is applied to efficiently treat the elastic body containing cracks, whereas the latter is adopted to handle both the adhesive layers and patches. The approximation of the near-front relative crack-face displacement is enhanced by using local interpolation functions that can capture the right asymptotic behavior. This also offers the direct calculation of the stress intensity factors along the crack front. A selected set of results is reported to demonstrate the capability of the proposed technique and the influence of various parameters on the performance of the strengthening.

Understanding seismic energy input and dissipation mechanism is necessary for energy-based seismic design of complex underground structures. Due to the intrinsic uncertainty of ground motion, stochastic methods are usually needed. In this paper, we study the seismic energy input and dissipation mechanism in an underground structure using the probability density evolution method (PDEM). It is found that the cumulative hysteretic energy dissipation ($E_h)$ of the underground structure is reduced by 55% compared with the above-ground structure due to soil constraint. The columns, walls and slabs at the bottom of the underground structure have a high demand for $E_h$, which are vulnerable spots of the structure.

Various types of machinery are not a continuous whole, but are assembled from various parts according to specific requirements. The surfaces that contact each other between different parts are often called mechanical joints. The stress/displacement field of the mechanical joint structure is the basis for predicting the mechanical properties of the assembly, optimizing the structure and the assembly process, and the existence of the mechanical joint surface destroys the continuity of the whole structure, which challenges the traditional calculation based on elastic mechanics. In view of the discontinuity of mechanical joints and the material difference of the parts matched with each other, this paper based on the layered elastic theory (LET), the discontinuity of the mechanical joint surface and the difference of the materials of the joint parts are analyzed. The mechanical joints are described by layers on the basis of the analysis of the discontinuity of typical mechanical joints. The stress and displacement equations are established by combining the surface characteristic parameters, and the established equations are solved by setting the boundary conditions. The calculation model of the stress/displacement field of the joint surface under the normal load is obtained. Finally, the model is used to calculate the experimental setting joint surface’s pressure distribution. In this paper, pressure distribution tests and finite element simulation are carried out on the joints with the same parameters. The results show that the model can accurately obtain the stress/displacement distribution law of the joints. The model can be directly used to calculate the pressure and displacement of the joint and the internal component. This model provides an effective method to analyze the stress and deformation of discontinuous structures, the distribution of pressure interface and the slip of interface. It can be directly used to calculate the joint position and the internal pressure and displacement of components, and the calculation efficiency is high.