Transient response of a transversely isotropic multilayered half-space due to a vertical loading

This paper investigates the transient response of a transversely isotropic multilayered half-space under vertical loadings. With the aid of a Laplace–Hankel transform, the global stiffness matrix for a multilayered half-space is acquired by assembling the analytical layer-element of each layer medium. The solutions for the displacements in the time domain are obtained by using the global stiffness matrix equations and a numerical inversion procedure. The accuracy of the proposed method is verified through comparisons with existing solutions for displacements induced by a step and rectangular pulse loading. In addition, selected numerical results for displacements induced by the buried loading are presented to illustrate the effect of transient loading type and material anisotropy on the transient response.     

多层厚壁圆筒频率方程的简化及一类贝塞尔函数递推公式

本文从理论上研究了相同材料的多层厚壁圆筒径向振动的频率方程,证明若干层相互接触的层筒的整体频率方程,可以用单个厚壁圆筒的频率方程替代,从而大大简化了求解过程.并从该实际问题出发,推导出了一类贝塞尔函数的递推公式.     

Numerical simulation of sphere water entry problem using Eulerian–Lagrangian method

This paper looks at the hydrodynamic’s numerical simulation of a free-falling sphere impacting the free surface of water by using the coupled Eulerian–Lagrangian (CEL) formulation included in the commercial software ABAQUS. A 3D model of a sphere with an unsteady viscous transient flow condition is used for numerical simulation. The simulation is performed for sphere with different density. The simulation results are verified by showing the computed shape of the air cavity, displacement of sphere, pinch-off time and depth that agree well with experimental results.     

Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations

In this paper the numerical approximations of the Ginzburg- Landau model for a superconducting hollow spheres are constructed using a gauge invariant discretization on spherical centroidal Voronoi tessellations. A reduced model equation is used on the surface of the sphere which is valid in the thin spherical shell limit. We present the numerical algorithms and their theoretical convergence as well as interesting numerical results on the vortex configurations. Properties of the spherical centroidal Voronoi tessellations are also utilized to provide a high resolution scheme for computing the supercurrent and the induced magnetic field.

     

Semianalytical methods for analyzing stress concentrations in thick-walled multilayered composites

For analyzing the stress, strain, and displacement fields in thick-walled anisotropic multilayered composites, sophisticated semianalytical solution methods based on a first-order shear deformation theory have been developed at the Insitut für Leichtbau und Kunststofftechnik and validated in a great number of numerical finite-element simulations and extensive experimental tests. A comparison of results obtained by the different methods for general multilayered composites made from unidirectional, bidirectional, and textile-reinforced layers show a good agreement.     

Transient piezothermoelastic analysis of a cross-ply laminated cylindrical panel bonded to a piezoelectric actuator

In this study, the theoretical treatment of transient piezothermoelastic problem is developed for a cross-ply laminated cylindrical panel bonded to a piezoelectric actuator due to nonuniform heat supply. By using the exact solutions for cross-ply laminate and piezoelectric layer of crystal class mm2, the theoretical analysis of a transient piezothermoelasticity is developed for a simple supported cylindrical composite panel under the state of plane strain. Analysis of a piezothermoelastic problem leads to an appropriate electric potential applied to the piezoelectric layer which suppresses the induced thermoelastic displacement in the radial direction at the midpoint on the free surface of the cross-ply laminate. Some numerical results for the temperature change, the displacement, the stress in a transient state when the transient thermoelastic displacement is controlled are shown in figures.     

Thermoelasticity of a Thermosensitive Hollow Anisotropic Sphere with a Thin Foreign Inclusion

By using generalized functions, we obtain the set of thermoelasticity equations for a hollow thermosensitive, transversally isotropic sphere with a thin foreign inclusion. By approximating the thermoelastic characteristics of the basic material and the material of the inclusion by piecewise-constant functions, we deduce a differential equation with coefficients of the type of impulse functions to determine a radial displacement. We carry out the numerical analysis of the temperature and level of thermal stresses in a system made of graphites.     

Three-dimensional exact thermo-elastic analysis of multilayered two-dimensional quasicrystal nanoplates

A three-dimensional thermo-elastic analytical solution for two-dimensional quasicrystal simply supported nanoplates subjected to a temperature change on their top surface is presented. The nonlocal theory and pseudo-Stroh formalism are used to obtain the exact solution for a homogeneous two-dimensional decagonal quasicrystal nanoplate with its thickness direction as a quasi-periodic direction. The propagator matrix method is introduced to deal with the corresponding multilayered nanoplates. Comprehensive numerical results show that nonlocal parameters, stress-temperature coefficients, stacking sequences have great influence on the stress, displacement components and heat fluxes of the nanoplates. In addition, the stacking sequences also influence the temperature and heat fluxes of the nanoplate. The exact thermo-elastic solution should be of interest to the design of the two-dimensional quasicrystal homogeneous and multilayered plates. The mechanical behaviors of the nanoplates in numerical results can also serve as benchmarks to verify various thin-plate theories or other numerical methods.     

Contact Problem for a Pneumatic Tire Interacting with a Rigid Foundation

Based on mixed finite-element approximations, a numerical algorithm is developed for solving a geometrically nonlinear contact problem for a prestressed multilayered Timoshenko-type shell undergoing arbitrarily large displacements and rotations. As unknowns, six displacements of faces of the shell are taken, which allows one to use principally new relationships for components of the Green–Lagrange strain tensor in curvilinear orthogonal coordinates, exactly representing arbitrarily large displacements of the shell as a rigid body. As an example, a tire interacting with a rigid foundation is considered.     

蠕动流中圆球阻力系数的入口效应

本文研究了圆球在半无穷长圆管入口处的蠕动流。得到了速度分布,压力分布和流函数的无穷级数形式的分析解.采用配置法将无穷级数截断并确定出级数中各项系数.求出了均匀入口流绕静止圆球以及圆球以瞬时速度在管内静止流体中运动这两种情形下圆球的阻力系数以及圆球表面上的应力分布.结果表明,当圆球在入口处运动时会遭受到较无穷圆管内为大的阻力.本文还对配置法的收敛性进行了数值实验.试验证明,该法具有好的收敛性.     

Limit analysis and numerical modeling of spherically porous solids with Coulomb and Drucker-Prager matrices

The first goal of this work was to develop efficient limit analysis (la) tools to investigate the macroscopic criterion of a porous material on the basis of the hollow sphere model used by Gurson, here with a Coulomb matrix. Another goal was to give the resulting rigorous lower and upper bounds to the macroscopic criterion to enable comparisons and validations with further analytical or numerical studies on this micro-macro problem. In both static and kinematic approaches of la, a quadratic formulation was used to represent the stress and displacement velocity fields, in triangular finite elements. A significant improvement of the quality of the results was obtained by superimposing, on the fem fields, analytical fields which are the solutions to the problem under isotropic loadings.The final problems result in conic optimization, or linear programming after linearization of the criterion, so as to determine the “Porous Coulomb” criterion. A fine iterative post-analysis strictly restores the admissibility of the static and kinematic solutions. After presenting the results for various values of the porosity and internal friction angle, a comparison with a heuristic Cam-Clay-like criterion shows that this criterion cannot be considered a precise general approximation. Then a comparison with the “Porous Drucker-Prager” criterion treated by specific 3D codes is presented. With the same numerical tools, a final analysis of recent results in the literature is detailed, and tables of selected numerical data are presented in the appendices.     

Non-axisymmetric consolidation of poroelastic multilayered materials with anisotropic permeability and compressible constituents

This paper presents an analytical layer-element solution to non-axisymmetric consolidation of multilayered poroelastic materials with anisotropic permeability and compressible constituents. By applying Fourier expansions, Hankel transforms and Laplace transforms to the state variables involved in the governing equations of poroelasticity with respect to the circumferential, radial and time coordinates, respectively, the analytical layer-element (i.e. a symmetric stiffness matrix) is derived, which describes the relationship between the transformed generalized stresses and displacements at the surface (z = 0) and those at an arbitrary depth z, considering the corresponding boundary and continuity conditions at the layer interfaces, the global stiffness matrix of a multilayered system is assembled in the transformed domain. The actual solutions in the physical domain are acquired by applying numerical quadrature schemes for the inversion of the Laplace–Hankel transform. Finally, numerical calculation is presented to investigate the influence of layering and poroelastic material parameters on consolidation process.     

Transient dynamics of composite sandwich plates using 4-, 8-, 9-noded isoparametric quadrilateral elements

A finite element method based on Mindlin's theory is employed in the prediction of the dynamic transient response of multilayered composite sandwich plates. Numerical convergence and stability of 4-noded linear, 8-noded serendipity, and 9-noded Lagrangian elements are established using an explicit time integration technique. A special mass matrix diagonalization scheme is adopted which conserves the total mass of the element and includes the effects due to rotary inertia terms. The parametric effects of the time step, finite element mesh, lamination scheme, and orthotropy on the transient response are investigated. Numerical results for deflections and stresses are presented under various boundary conditions and loadings. The results presented herein should be of interest to composite-structure designers, experimentalists, and numerical analysists in verifying their results.     

Three-dimensional Green's functions of thermoporoelastic axisymmetric cones

On the base of Biot's consolidation theory, we introduce the steady-state general solutions of thermoporoelastic axisymmetric media initially. Several three-dimensional problems of porous media, such as the apex of a solid cone and a hollow cone under the action of a point fluid source and a point heat source in a steady state, are analyzed afterwards, respectively. By introducing the potential functions with the coefficients determined in line with the corresponding liquid-heat-force equilibrium relations and boundary conditions, we obtain the coupled fields of thermoporoelastic cones suffered from the point sources. Furthermore, the numerical examples as well as the contour plots of the coupled fields of thermoporoelastic cones are presented. The numerical results show that the phenomenon of stress concentration can occur near the point of action. The results associated with the apex angle π/2 are of importance to be used for constructing the analytical solutions of the boundary value problems as well as the defect problems.     

Numerical simulation of rotational symmetric tube bulging with inside pressure and axial compression

The contribution treats the process of rotational symmetric tube bulging with inside pressure and axial compression. This process enables the standard tubes to be formed into different rotational symmetric hollow parts in such a way that their central part is expanded into a desired shape while the ends remain unchanged. The superposition of axial compression contributes to a more favourable forming stress state, which is reflected in larger forming limits and smaller wall thinning in the widened area. The problems characterizing the process are a limited range of compression stability and difficulties met when establishing and optimizing the technological parameters of the process whose course cannot be defined in an analytical way. Based on a physical model of the forming process, a numerical model was built. Using ABAQUS code the model was simulated over the entire stress/forming region. A comparison of the computer simulated forming process with the experimentally obtained results showed that the model was highly accurate.     

Three-dimensional exact solution of layered two-dimensional quasicrystal simply supported nanoplates with size-dependent effects

A size-dependent plate model is developed to investigate the elastic responses of the multilayered two-dimensional quasicrystal nanoplates based on the nonlocal strain gradient theory for the first time. A nonlocal stress field parameter and a length scale parameter are taken into account in the new model to capture both stiffness-softening and stiffness-hardening size effects. The exact solution for a single-layer two-dimensional quasicrystal simply supported nanoplate is derived by utilizing the pseudo-Stroh formalism in conjunction with the nonlocal strain gradient theory. Afterward, a dual variable and position method is used to deal with the multilayered case. Numerical examples are presented to study the dependence of size-dependent effect on nanoplate length and the influences of scale parameters on the quasicrystal nanoplate subjected to a z-direction mechanical load on its top surface. The proposed model should be useful to verify various nanoplate theories and other numerical methods.     

Numerical–analytical model for transient dynamics of elastic-plastic plate under eccentric low-velocity impact

The aim of this study is to present an efficient model for the analysis of complicated nonlinear transient dynamics of an elastic-plastic plate subjected to a transversely eccentric low-velocity impact. A mixed numerical–analytical model is presented to predict the transient dynamic behaviours consisting of either plate impact responses or wave propagations induced by the impact in a plate with an arbitrary shape and support. This hybrid approach has been validated by comparison with results of laboratory tests performed on an elastic-perfectly plastic narrow plate eccentrically struck by an elastic sphere, and results of a three-dimensional finite element (FE) analysis for an elastic-perfectly plastic simply-supported rectangular plate eccentrically struck by an elastic sphere. The advantages of this hybrid approach are in the simplification of local contact force formulation, computational efficiency over the FE model, and convenient application to parametric study for eccentric impact behaviour. The hybrid approach can provide accurate predictions of the plate impact responses and plate wave propagations.     

Real-time simulation of thermal stresses and creep in plates subjected to transient heat input

This paper presents a novel numerical technique for solvingthe temperature and stress fields in a plate subjected to arbitrarilyvarying transient boundary conditions (transient temperatureand heat-flux variations) on a surface. The numerical methodis based on the control-volume finite-difference approach. Itapplies a general formulation which takes into account nonconstantmaterial properties (e.g. temperature, material, or time dependency),heat-transfer coefficients, and creep. The temperature calculationapplies a one-dimensional numerical model, whereas the stressanalysis is semi-two-dimensional. Both plane stress and planestrain conditions are considered as extreme cases. It is shownthat, by using the developed numerical technique, very fastreal-time simulations can be performed. The method has provedits applicability in e.g. high-pressure die-casting, and applicationsto this industrial process are considered.     

压电弹性动力学中第二类Volterra积分方程的数值解法

对于径向变形的压电空心圆柱和空心球弹性动力学问题,丁皓江等最近的研究表明,可以将它转变为关于一个时间函数的第二类Volterra积分方程,使求解工作得到极大的简化,又使探索第二类Volterra积分方程的快速而又高精度的数值解法成为一个关键．采用插值逼近方法,成功地导出了两个新型的递推公式,不仅计算速度快,且在较大时间步长时仍具有足够的精度,有着广泛的应用价值．