An efficient simple element for free vibration and buckling analysis of FG beam

In this paper, a simple and efficient element is proposed for the free vibration and buckling analysis of FGM beams. This element is formulating, based on Timoshenko beam theory. The assumption of constant shear strain in the element reduces the number of unknowns in addition to improving the efficiency of the new element. The performance of the new element is evaluated with the help of several benchmark tests. First, the accuracy and convergence rate of the proposed element response in the analysis of free vibration and buckling of the beam are investigated separately by exponential variations of the modulus of elasticity and density in each of the beams' thickness and length. Subsequently, the element's ability to model material variations in both longitudinal and thickness directions of the beam will be measured simultaneously. For comparison, the answers of good elements of other researchers are available in each of the numerical tests. These tests will prove the high accuracy and rapid convergence rate of the proposed element.

A Cooperative Coevolution Wingsuit Flying Search Algorithm with Spherical Evolution

The algorithm wingsuit flying search (WFS) mimics the procedure of landing the vehicle. The outstanding feature of WFS is parameterless and of rapid convergence. However, WFS also has its shortcomings, sometimes it will inevitably be trapped into local optima, thereby yield inferior solutions owing to its relatively weak exploration ability. Spherical evolution (SE) adopts a novel spherical search pattern that takes aim at splendid search ability. Cooperative coevolution is a useful parallel structure for reconciling algorithmic performance. Considering the complementary strengths of both algorithms, we herein propose a new hybrid algorithm that is comprised of SE and WFS using cooperative coevolution. During the search for optimal solutions in WFS, we replaced the original search matrix and introduced the spherical mechanism of SE, in parallel with coevolution to enhance the competitiveness of the population. The two distinct search dynamics were combined in a parallel and coevolutionary way, thereby getting a good search performance. The resultant hybrid algorithm, CCWFSSE, was tested on the CEC2017 benchmark set and 22 CEC 2011 real-world problems. The experimental data obtained can verify that CCWFSSE outperforms other algorithms in aspects of effectiveness and robustness.

HybridCTrm: Bridging CNN and Transformer for Multimodal Brain Image Segmentation

Multimodal medical image segmentation is always a critical problem in medical image segmentation. Traditional deep learning methods utilize fully CNNs for encoding given images, thus leading to deficiency of long-range dependencies and bad generalization performance. Recently, a sequence of Transformer-based methodologies emerges in the field of image processing, which brings great generalization and performance in various tasks. On the other hand, traditional CNNs have their own advantages, such as rapid convergence and local representations. Therefore, we analyze a hybrid multimodal segmentation method based on Transformers and CNNs and propose a novel architecture, HybridCTrm network. We conduct experiments using HybridCTrm on two benchmark datasets and compare with HyperDenseNet, a network based on fully CNNs. Results show that our HybridCTrm outperforms HyperDenseNet on most of the evaluation metrics. Furthermore, we analyze the influence of the depth of Transformer on the performance. Besides, we visualize the results and carefully explore how our hybrid methods improve on segmentations.

Efficient Modification of the Decomposition Method for Solving a System of PDEs

This paper presents an analysis solution for systems of partial differential equations using a new modification of the decomposition method to overcome the computational difficulties. Convergence of series solution was discussed with two illustrated examples, and the method showed a high-precision, being a fast approach to solve the non-linear system of PDEs with initial conditions. There is no need to convert the nonlinear terms into the linear ones due to the Adomian polynomials. The method does not require any discretization or assumption for a small parameter to be present in the problem. The steps of the suggested method are easily implemented, with high accuracy and rapid convergence to the exact solution, compared with other methods that can be used to solve systems of PDEs.

Numerical solution of large deflection beams by using the Laplace Adomian decomposition method

PurposeThis paper presents the problems using Laplace Adomian decomposition method (LADM) for investigating the deformation and nonlinear behavior of the large deflection problems on Euler-Bernoulli beam.Design/methodology/approachThe governing equations will be converted to characteristic equations based on the LADM. The validity of the LADM has been confirmed by comparing the numerical results to different methods.FindingsThe results of the LADM are found to be better than the results of Adomian decomposition method (ADM), due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms. LADM are presented for two examples for large deflection problems. The results obtained from example 1 shows the effects of the loading, horizontal parameters and moment parameters. Example 2 demonstrates the point loading and point angle influence on the Euler-Bernoulli beam.Originality/valueThe results of the LADM are found to be better than the results of ADM, due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms.

Jacobian Consistency of a Smoothing Function for the Weighted Second-Order Cone Complementarity Problem

In this paper, a weighted second-order cone (SOC) complementarity function and its smoothing function are presented. Then, we derive the computable formula for the Jacobian of the smoothing function and show its Jacobian consistency. Also, we estimate the distance between the subgradient of the weighted SOC complementarity function and the gradient of its smoothing function. These results will be critical to achieve the rapid convergence of smoothing methods for weighted SOC complementarity problems.

Codimension bounds and rigidity of ancient mean curvature flows by the tangent flow at −∞

Motivated by the limiting behavior of an explicit class of compact ancient curve shortening flows, by adapting the work of Colding–Minicozzi [11], we prove codimension bounds for ancient mean curvature flows by their tangent flow at [Formula: see text]. In the case of the [Formula: see text]-covered circle, we apply this bound to prove a strong rigidity theorem. Furthermore, we extend this paradigm by showing that under the assumption of sufficiently rapid convergence, a compact ancient mean curvature flow is identical to its tangent flow at [Formula: see text].