Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element

The modulus of elasticity of some materials changes under tensile and compressive states is simulated by constructing a typical material nonlinearity in a numerical analysis in this paper. The meshless Finite Block Method (FBM) has been developed to deal with 3D semi-infinite structures in the bimodular materials in this paper. The Lagrange polynomial interpolation is utilized to construct the meshless shape function with the mapping technique to transform the irregular finite domain or semi-infinite physical solids into a normalized domain. A shear modulus strategy is developed to present the nonlinear characteristics of bimodular material. In order to verify the efficiency and accuracy of FBM, the numerical results are compared with both analytical and numerical solutions provided by Finite Element Method (FEM) in four examples.

Synchronized Assessment of Bridge Structural Damage and Moving Force via Truncated Load Shape Function

Moving load and structural damage assessment has always been a crucial topic in bridge health monitoring, as it helps analyze the daily operating status of bridges and provides fundamental information for bridge safety evaluation. However, most studies and research consider these issues as two separate problems. In practice, unknown moving loads and damage usually coexist and influence the bridge vibration synergically. This paper proposes an innovative synchronized assessment method that determines structural damages and moving forces simultaneously. The method firstly improves the virtual distortion method, which shifts the structural damage into external virtual forces and hence transforms the damage assessment as well as the moving force identification to a multi-force reconstruction problem. Secondly, a truncated load shape function (TLSF) technique is developed to solve the forces in the time domain. As the technique smoothens the pulse function via a limited number of TLSF, the singularity and dimension of the system matrix in the force reconstruction is largely reduced. A continuous beam and a three-dimensional truss bridge are simulated as examples. Case studies show that the method can effectively identify various speeds and numbers of moving loads, as well as different levels of structural damages. The calculation efficiency and robustness to white noise are also impressive.

Solving nonlinear boundary value problems by a boundary shape function method and a splitting and linearizing method

In the paper, we develop two novel iterative methods to determine the solution of a second-order nonlinear boundary value problem (BVP), which precisely satisfies the specified non-separable boundary conditions by taking advantage of the property of the corresponding boundary shape function (BSF). The first method based on the BSF can exactly transform the BVP to an initial value problem for the new variable with two given initial values, while two unknown terminal values are determined iteratively. By using the BSF in the second method, we derive the fractional powers exponential functions as the bases, which automatically satisfy the boundary conditions. A new splitting and linearizing technique is used to transform the nonlinear BVP into linear equations at each iteration step, which are solved to determine the expansion coefficients and then the solution is available. Upon adopting those two novel methods very accurate solution for the nonlinear BVP with non-separable boundary conditions can be found quickly. Several numerical examples are solved to assess the efficiency and accuracy of the proposed iterative algorithms, which are compared to the shooting method.

The Improved Interpolating Dimension Splitting Element-Free Galerkin Method for 3D Potential Problems

This paper proposes the improved interpolating dimension splitting element-free Galerkin (IIDSEFG) method based on the nonsingular weight function for three-dimensional (3D) potential problems. The core of the IIDSEFG method is to transform the 3D problem domain into a series of two-dimensional (2D) problem subdomains along the splitting direction. For the 2D problems on these 2D subdomains, the shape function is constructed by the improved interpolating moving least-squares (IIMLS) method based on the nonsingular weight function, and the finite difference method (FDM) is used to couple the discretized equations in the direction of splitting. Finally, the calculation formula of the IIDSEFG method for a 3D potential problem is derived. Compared with the improved element-free Galerkin (IEFG) method, the advantages of the IIDSEFG method are that the shape function has few undetermined coefficients and the essential boundary conditions can be executed directly. The results of the selected numerical examples are compared by the IIDSEFG method, IEFG method and analytical solution. These numerical examples illustrate that the IIDSEFG method is effective to solve 3D potential problems. The computational accuracy and efficiency of the IIDSEFG method are better than the IEFG method.

Pilegrimsspor fra Tynset: En detektorfunnet blymedaljong med kristne motiver

In 2016, a metal detectorist found a circular lead medallion with iconography on both sides in Tynset in the Østerdalen valley. This article studies the medallion’s shape, function and symbolical content. The object is interpreted as a pendant comparable with pilgrim badges from the late medieval period. The motifs are identified as Christian, representing the apocalyptical Mary with Christ on one side, and a passion and resurrection scene on the other. In this article, the medallion is compared to Norwegian and other European pilgrim badges and amulets with the same motifs, suggesting its origin most likely to be Aachen in Germany. Aachen was one of the most visited holy places for pilgrimage in Europe. The motifs can be connected to the Marian cathedral in Aachen, at the same time as expressing religious content regularly transmitted in the late medieval church. By comparing the motifs with Old Norse texts and images, the article demonstrates how the amulet’s religious messages potentially could influence the bearer – possibly a Norwegian pilgrim.

Traversable wormhole solutions with non-exotic fluid in framework of f(Q) gravity

The presence of exotic matter for the existence of the wormhole geometry has been an unavoidable problem in GR. In recent studies, researchers have tried to deal with this issue using modified gravity theories where the WH geometry is explained by the extra curvature terms and NEC’s are not violated signifying the standard matter in the WH geometry. In this paper, we investigate the solutions of traversable wormholes with normal matter in the throat within the framework of symmetric teleparallel gravity [Formula: see text], where [Formula: see text] is the non-metricity scalar that defines the gravitational interaction. We analyze the wormhole geometries for three forms of function [Formula: see text]. First is the linear form [Formula: see text], second a nonlinear form [Formula: see text] and third one a more general quadratic form [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text] being the constants. For all the three cases, the shape function is taken as [Formula: see text] where [Formula: see text] is the throat radius. A special variable redshift function is considered for the discussion. All the energy conditions are then examined for the existence and stability of the wormhole geometry.

Solution of the Static Deflection Mode Shape Function of the Cantilever Beam under Transverse Flow Based on the Boundary Shooting Method

According to the characteristics of the reactor internal structure of nuclear power plants, the vibration of the secondary core support pillar in water can be modeled as the vibration of the cantilever beam structure under the action of transverse flow, and its first beam mode is highly likely to be activated. It is thus necessary to dedicate a separate study on the first-order beam mode. In this work, we study the secondary core support pillar in nuclear reactor AP1000 under the action of transverse flow and focus on the derivation of its static cantilever deflection mode shape function in order to lay a foundation for the calculation of hydrodynamic added mass and frequency for the nuclear reactor internal components and their structural integrity evaluation. First, we proposed a set of nonlinear differential equations for the analysis of the single cantilever beam. Second, to solve the nonlinear differential equations, we used a boundary shooting framework in combination with the Runge–Kutta method. The results of the numerical simulation agree with the analytical solution to a very high degree, which demonstrates the effectiveness of the simulation method. Finally, we solved the static deflection mode shape function of the secondary core support pillar under the normal operating conditions. The nonlinear differential model and simulation method proposed in this paper can be used to solve the static cantilever deflection mode shape function of the equipment support tube.