卵形弹垂直侵彻混凝土介质的量纲分析

针对卵形弹侵彻半无限厚混凝土介质,采用量纲分析的方法建立了相关参数的无量纲化的函数关系,通过质量为2.85kg,弹径为50.8mm的卵形弹垂直侵彻混凝土实验确定撞击混凝土侵深的工程表达式.     

Reply to “Comments on “Model for cover cracking due to corrosion expansion and uniform stresses at infinity””

Corrosion of rebar in concrete under service conditions is a dynamic, continuous and interaction process between rebar, corrosion products and concrete. Both the penetration depth and the rate of penetration are functions of time.     

Mathematical modeling of temperature pulsation in a thick anode in optoelectronic systems

A numerical method is applied to analyze the one-dimensional model of temperature pulsation inside a two-layer anode with temperature-dependent thermophysical coefficients. The analysis allows for surface thermal radiation, secondary electron emission, and distribution of electron energy losses by penetration depth into the target. Penetration of pulsations deep into the target is observed.Translated from Matematicheskoe Modelirovanie i Reshenie Obratnykh Zadach Matematicheskoi Fiziki, pp. 215–217, 1993.     

弹侵彻混凝土靶的法向膨胀理论

基于描述材料在高速高压冲击下的动态行为的方程,建立了相应的冲击波前为一般曲面的方程．通过分析,针对混凝土材料,提出了可给出弹体减速度时间历程解析解的法向膨胀理论．它不仅适用于球形弹头和柱形弹头,也适用于其他类型的弹头,如锥形弹头和卵形弹头等;它不但适用于垂直侵彻,也适用于斜侵彻．     

陶瓷/金属复合靶板受可变形弹体撞击的理论分析模型

针对弹体撞击陶瓷/金属复合靶板的问题,将弹体的变形、陶瓷面板的碎裂和金属背板的变形结合起来,建立了新的可变形弹体垂直撞击陶瓷/金属靶板的理论分析模型．模型中计入了弹体刚性区长度和运动速度、塑性变形区长度、横截面积和运动速度的变化以及弹体对靶板的侵入速度和深度;对陶瓷面板考虑了陶瓷锥体积和抗压强度的变化;对金属背板的变形,根据其塑性变形功、外力功及其动能守恒原理,得到金属背板的运动方程．最后对具体算例进行了分析,得到了各物理量随时间的变化,给出了一些有价值的规律．结果表明,模型能较好地描述撞击过程中的有关规律;与实验结果和数值模拟结果进行对比,吻合较好,说明了模型的有效性．     

Theoretical analysis of numerical integration in Galerkin meshless methods

In this paper, we study effects of numerical integration on Galerkin meshless methods for solving elliptic partial differential equations with Neumann boundary conditions. The shape functions used in the meshless methods reproduce linear polynomials. The numerical integration rules are required to satisfy the so-called zero row sum condition of stiffness matrix, which is also used by Babuška et al. (Int. J. Numer. Methods Eng. 76:1434–1470, 2008). But the analysis presented there relies on a certain property of the approximation space, which is difficult to verify. The analysis in this paper does not require this property. Moreover, the Lagrange multiplier technique was used to handle the pure Neumann condition. We have also identified specific numerical schemes, diagonal elements correction and background mesh integration, that satisfy the zero row sum condition. The numerical experiments are carried out to verify the theoretical results and test the accuracy of the algorithms.     

A model for taking into account the nonlinearity of properties of a semifinished product in the force analysis of the winding of composite materials

Conclusions 1. The proposed method of accounting for the nonlinearity of properties of a semifinished product by a piecewise-linear approximation of its stress—strain diagram greatly refines the calculation of stresses induced during the process of winding a product.2. A numerical analysis has revealed the ranges of values of the winding parameters where replacing the nonlinear model by simpler linear models for the calculation is appropriate.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 231–240, March–April, 1977.     

Premature in-bore separation of sabot-jacketed projectiles

The premature separation of saboted projectiles undergoing high-mach-number in-bore acceleration is investigated. Results from a simplified numerical model for the problem are presented. Measured short-term velocity history for a typical projectile is used to describe the motion of a nonuniformly accelerating piston. Two numerical algorithms for calculating the shocked flow in tront of the accelerating piston are presented. Mach number and pressure time histories for the flow afford corrective input to the sabot design process. © 1993 John Wiley & Sons, Inc.     

HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet

In the present study, we have described the stagnation point flow of a viscous fluid towards a stretching sheet. The complete analytical solution of the boundary layer equation has been obtained by homotopy analysis method (HAM). The solutions are compared with the available numerical results obtained by Nazar et al. [Nazar R, Amin N, Filip D, Pop I. Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet. Int J Eng Sci 2004;42:1241–53] and a good agreement is found. The convergence region is also computed which shows the validity of the HAM solution.     

A hybrid-Trefftz element containing an elliptic hole

Much work on special elements that simplify geometrical modelling of structures containing holes, cracks and/ or inclusions has been reported extensively in the literature. This paper presents a hybrid-Trefftz element containing elliptic hole formulated using Hellinger–Reissner principle by employing trial functions based on the mapping technique and the Cauchy integral method. The element presented in this paper could be regarded as an improved formulation over Piltner [Special finite elements with holes and internal cracks, Int. J. Numer. Methods Eng. 21 (1985) 1471–1485] element because the chosen trail functions in this paper have provided relatively more stable solutions. The use of the element with other ordinary displacement-based finite elements has also yielded very accurate solutions even when very coarse meshes relative to the size of the elliptic hole have been used.     

Prediction of the penetrated rust into the microcracks of concrete caused by reinforcement corrosion

Consider a steel-rust-concrete composite consisting of a circular cylindrical concrete cover and a coaxial uniformly corroding steel reinforcement. Prediction of the amount of rust penetrated into the microcracks of concrete cover from a set of data measured at the surface of the concrete is of particular interest. The steel is assumed to be linear isotropic and rust follows a power law stress–strain relation. For the concrete, anisotropic behavior and post-cracking softening model is employed. The formulations lead to a nonlinear boundary value problem which is solved analytically. A key parameter β, defined as the ratio of the volume of corrosion products inside the cracks to the volume of the cracks, is calculated. With some efforts, this parameter is also extracted from the available theoretical and experimental studies for the purpose of comparison. The effects of the mechanical properties of rust and concrete on β is addressed.     

Least‐square collocation and Lagrange multipliers forTaylor meshless method

A recently proposed meshless method is discussed in this article. It relies on Taylor series, the shape functions being high degree polynomials deduced from the Partial Differential Equation (PDE). In this framework, an efficient technique to couple several polynomial approximations has been presented in (Tampango, Potier‐Ferry, Koutsawa, Tiem, Int. J. Numer. Meth. Eng. vol. 95 (2013) pp. 1094–1112): the boundary conditions were applied using the least‐square collocation and the interface was coupled by a bridging technique based on Lagrange multipliers. In this article, least‐square collocation and Lagrange multipliers are applied for boundary conditions, respectively, and least‐square collocation is revisited to account for the interface conditions in piecewise resolutions. Various combinations of these two techniques have been investigated and the numerical results prove their effectiveness to obtain very accurate solutions, even for large scale problems.     

Evolution of the Stress–Strain State of a Three-Dimensional Plate Weakened by a Central Crack under Impulsive Tension

A method is developed to describe the formation of the stress–strain state in the vicinity of the tip of a stationary crack in a three-dimensional plate under dynamic loading. The energy model used to describe the formation of the stress concentration zone around the crack tip is modified to take into account the transient character of the loading process and the influence of the free surfaces of the plate on the stress–strain state of the central part of the sample. The method is useful for describing static and dynamic brittle fracture from a unified point of view.     

Comments on “Model for cover cracking due to corrosion expansion and uniform stresses at infinity”

This paper presents a discussion on a model for cover cracking due to corrosion expansion and uniform stress at infinity developed by Li et al. [Shu-cai Li, Ming-bin Wang, Shu-chen Li, Model for cover cracking due to corrosion expansion and uniform stresses at infinity, Appl. Math. Modell., doi:10.1016/j.apm.2007.06.003]. The model for cover cracking by the authors uses an equation of the penetration depth of corrosion with time developed from the Faraday’s Law. It is however shown in the discussion that the equation of the penetration depth due to corrosion developed by Li et al. is incorrect. Consequently other equations developed by Li et al. to model cover cracking that use the equation of penetration depth are also incorrect.     

Projection stabilization of Lagrange multipliers for the imposition of constraints on interfaces and boundaries

Projection stabilization applied to general Lagrange multiplier finite element methods is introduced and analyzed in an abstract framework. We then consider some applications of the stabilized methods: (i) the weak imposition of boundary conditions, (ii) multiphysics coupling on unfitted meshes, (iii) a new interpretation of the classical residual stabilized Lagrange multiplier method introduced in Barbosa and Hughes, Comput Methods Appl Mech Eng 85 (1991), 109–128. © 2013 The Authors. Numerical Methods for Partial Differential Equations Published by Wiley Periodicals, Inc. 30: 567–592, 2014     

Consideration of friction between layers in determining the stress-strain state of structures with nonideal layer contact

A mathematical model for calculation of structures in a three-dimensional installation allowing for layer slippage with friction was constructed. The examples examined show that consideration of friction in problems of calculating laminated structures with nonideal layer contact can introduce an essential correction in the stress—strain state of the structure. In slabs with a freely sagging lower surface, friction is perceived for important friction coefficients and increases when the slippage surface approaches the loaded surface. In masses with a rigidly attached lower surface, even insignificant friction coefficients lead to essential redistribution of the stress—strain state.Ukraine Transportation University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 192–199, March–April, 1997.     

Chaos in a three-species food chain model with a Beddington–DeAngelis functional response

This paper investigates a three-species food chain model with a Beddington–DeAngelis functional response, both analytically and through numerical simulations. First the equilibrium states of the system are identified and their stability analyzed analytically. The results of simulations demonstrate chaotic long-term behavior over a broad range of parameters. The existence of a strange attractor and computation of the largest Lyapunov exponent also demonstrate the presence of chaotic dynamics in the model.     

半参数两样本密度比率模型估计问题的一点注记

In this paper,a semiparametric two-sample density ratio model is considered and the empirical likelihood method is applied to obtain the parameters estimation.A commonly occurring problem in computing is that the empirical likelihood function may be a concaveconvex function.Here a simple Lagrange saddle point algorithm is presented for computing the saddle point of the empirical likelihood function when the Lagrange multiplier has no explicit solution.So we can obtain the maximum empirical likelihood estimation (MELE) of parameters.Monte Carlo simulations are presented to illustrate the Lagrange saddle point algorithm.