Numerical analysis of finite amplitude motion of waves and a moored floating body under severe storm conditions

The motion of a moored floating body under the action of wave forces, which is influenced by fluid forces, shape of the floating body and mooring forces, should be analysed as a complex coupled motion system. Especially under severe storm conditions or resonant motion of the floating body it is necessary to consider finite amplitude motions of the waves, the floating body and the mooring lines as well as non-linear interactions of these finite amplitude motions. The problem of a floating body has been studied on the basis of linear wave theory by many researchers. However, the finite amplitude motion under a correlated motion system has rarely been taken into account. This paper presents a numerical method for calculating the finite amplitude motion when a floating body is moored by non-linear mooring lines such as chains and cables under severe storm conditions.     

空化起始的理论预测——模糊空化系统

木文建立了一个模糊空化系统、运用模糊数学的理论对空化起始问题进行了理论预测、根据反映空化核群空化行为的四个空化特征值和由试验得出的一些定性规律,用模糊理论的方法得出控制系统空化状态的模糊状态转移矩阵,从而估算出系统的空化状态。用本文所提出的方法对两种轴对称头体的空化起始进行了预测。所得的结果与相应的试验结果相当满意地符合。     

Pairwise Deformations of an Incompressible Elastic Body under Dead-Load Tractions

In this paper we obtain necessary conditions for the existence of pairwise deformations of an incompressible, isotropic elastic body subjected to a homogeneous distribution of dead-load tractions. Explicit restrictions on the boundary loads and on the surface of discontinuity between the phases are determined. For hyperelastic bodies with stored energy depending only on the first invariant of strain, we show that pairwise deformations under examination are necessarily (within a rigid rotation) plane deformations.     

Motions of a top on a smooth plane without separation

The problem on the motion of a heavy top (a dynamically and geometrically symmetric rigid body) without separation on a smooth horizontal plane is considered. In the case of a spherical top surface (the Thomson top), necessary and sufficient conditions on the parameters and the initial positions and velocities of the body under which the motion is all the time without separation are given. These conditions are represented by explicit analytic formulas that can be used in practice. Keywords: Thomson top, smooth surface, separation conditions.     

On the dynamical symmetry points and the orientations of the principal axes of inertia of a rigid body

For an arbitrary rigid body, all dynamical symmetry points are found, and the directions of the axes of dynamical symmetry are determined for these points. We obtain conditions on the principal central moments of inertia under which the Lagrange and Kovalevskaya cases can be realized for the rigid body. We also analyze the set of orientations of the bases formed by the principal axes of inertia for various points of the rigid body.     

GENERALIZED VARIATIONAL PRINCIPLESFOR VISCOELASTIC THIN AND THICK PLATES WITH DAMAGE

From the constitutive model with generalized force fields for a viscoelastic body with damage, the differential equations of motion for thin and thick plates with damage are derived under arbitrary boundary conditions. The convolution-type functionals for the bending of viscoelastic thin and thick plates with damage are presented, and the corresponding generalized variational principles are given. From these generalized principles, all the basic equations of the displacement and damage variables and initial and boundary conditions can be deduced. As an example, we compare the difference between the dynamical properties of plates with and without damage and consider the effect of damage on the dynamical properties of plates.     

Mathematical modeling of volumetric material growth

Growth (resp. atrophy) describes the physical processes by which a material of solid body increases (resp. decreases) its size by addition (resp. removal) of mass. In the present contribution, we propose a sound mathematical analysis of growth, relying on the decomposition of the geometric deformation tensor into the product of a growth tensor describing the local addition of material and an elastic tensor, which is characterizing the reorganization of the body. The Blatz-Co hyperelastic constitutive model is adopted for an isotropic body, satisfying convexity conditions (resp. concavity conditions) with respect to the transformation gradient (resp. temperature). The evolution law for the transplant is obtained from the natural assumption that the evolution of the material is independent of the reference frame. It involves a modified Eshelby tensor based on the specific free energy density. The heat flux is dependent upon the transplant. The model consists of the constitutive equation, the energy balance, and the evolution law for the transplant. It is completed by suitable boundary conditions for the displacement, temperature and transplant tensor. The existence of locally unique solutions is obtained, for sufficiently smooth data close to the stable equilibrium. The question of the global existence is examined in the simplified situation of quasistatic isothermal equations of linear elasticity under the assumption of isotropic growth.     

发射药燃烧热辐射传播规律

采用构建物理数学模型和实验验证的方法,首次提出发射药燃烧热辐射柱体理论模型;利用自由场条件下的单基发射药燃烧热辐射实验,对比分析球体热辐射模型,验证了柱体理论模型能够客观反映发射药燃烧热辐射传播规律。实验表明,自由场条件下4种不同单基发射药药量的燃烧热辐射实验数据与柱体燃烧理论模型相吻合;同时由数据拟合分别得到单基发射药热通量与药量、距离以及热剂量与药量、距离的定量函数关系,可为准确评估单基发射药燃烧热辐射毁伤效应提供相关理论基础。

     

Attitude stabilization of a rigid body under the action of a vanishing control torque

The problem of attitude stabilization of a rigid body with the use of restoring and dissipative torques is studied. The possibility of implementing a control system in which the restoring torque tends to zero as time increases, and the only remaining control torque is a linear time-invariant dissipative one, is investigated. Both cases of linear and essentially nonlinear restoring torques are considered. With the aid of the Lyapunov direct method and the comparison method, conditions are derived under which we can guarantee stability or asymptotic stability of an equilibrium position of the body despite the vanishing of the restoring torque. A numerical simulation is provided to demonstrate the effectiveness of analytical results.     

Analysis of a rigid body obliquely impacting granular matter

The model of the oblique rigid body impact with a granular matter is studied. The force acting on the body is a linear superposition of a static (velocity-independent) friction force and a dynamic (velocity-dependent) resistance force. The impact of a sphere, a mathematical and a compound pendulum are modeled and simulated using different initial impact velocity conditions and different impact angles. We analyze how rapidly the rigid body impacting a granular media slows upon collision. For most of the analyzed cases the rigid body under high-force impact (higher initial velocity) comes to rest faster in a granular matter than the same body under low-force impacts (lower initial velocity). Researchers were able to explain this interesting phenomena, not shared by solids or liquids, for the vertical impact of spheres. The simulations for some configurations with small initial impact angles show that as the speed at which the rigid body impacts the media increases, the later it will come to rest.

     

The Stability in Two Measures of Axially Compressed Elastic Cylinders

Two nonnegative integral functionals are taken as measures of deviation of the basic solution from a perturbed one. Sufficient conditions of stability in selected measures are obtained for the zero solution of the linearized equation of motion for isotropic elastic bodies acted upon by "dead" surface forces. The method of integral estimates is used to determine the critical values of the loading parameters. Such values are found for an axially compressed cylindrical body made of a standard material of the second order under various end conditions     

A Mathematical Model for Short-Time Filtration in Poroelastic Media with Thermal Relaxation and Two Temperatures

In this work, we derive a set of governing equations for a mathematical model of generalized thermoelasticity in poroelastic materials. This model predicts finite speeds of propagation of waves contrary to the model of coupled thermoelasticity where an infinite speed of propagation is inherent. Next, we prove the uniqueness of solution of these equations under suitable conditions. We also obtain a reciprocity theorem for these equations. A thermal shock problem for a half-space composed of a poroelastic material saturated with a liquid is then considered. The surface of the half-space is assumed to be traction free, permeable, and subjected to heating. The Laplace transform technique is used to solve the problem. Numerical results for the temperature in the elastic body and fluid, displacement of the elastic body, velocity of the fluid, and stresses for both components are obtained and represented graphically.     

A dynamic gait stabilization algorithm for quadrupedal locomotion through contact time modulation

In this paper, we propose a stabilization method for dynamic gaits of quadrupedal walking robots covering a wide range of speeds and various types of gait. Our stabilization method is based on adjusting the contact time between the four legs and ground. By modulating the contact time, the impact applied to the body can be controlled and stabilized. The stability provided by the proposed algorithm was proved in the sense of Lyapunov. The proposed algorithm also demonstrated robust performance under large external disturbances, and the performance was compared with other algorithms through simulations. Simulation results of bounding gaits under different ground conditions were compared, and the various types of stable gait implemented by the proposed algorithm are also presented.

     

Intensity of singular stress fields causing interfacial debonding at the end of a fiber under pullout force and transverse tension

In this study, singular stress fields at the ends of fibers are discussed by the use of models of rectangular and cylindrical inclusions in a semi-infinite body under pullout force. Those singular stresses have not been discussed yet in the previous studies for pullout problems although they are important for causing interfacial initial debonding. The body force method is used to formulate those problems as a system of singular integral equations where unknowns are densities of the body forces distributed in a semi-infinite body having the same elastic constants as those of the matrix and inclusions. In order to compare the results with the previous solutions, tension problems of a fiber in a semi-infinite body are also considered. Then, generalized stress intensity factors at the corner of rectangular and cylindrical inclusions are systematically calculated for various geometrical conditions with varying the elastic ratio, length, and spacing of the location from edge to inner of the body. The effects of elastic modulus ratio and aspect ratio of inclusion upon the stress intensity factors are discussed for pullout problems.     

横观各向同性热弹性梁的精化理论

本文从横观各向同性梁的二维问题出发,研究了横观各向同性热弹性梁的精化理论。首先,在不作任何预先假设的条件下,利用横观各向同性热弹性理论和Lur’e算子函数,获得了由梁中线上的物理量表示的位移场和应力场。对热弹性梁上下表面承受非齐次边界条件的情况,推导出梁的近似控制微分方程。再舍去温度项,则横观各向同性热弹性梁的精化理论退化为横观各向同性梁的精化理论。     

Fracture of circular plates on normal impact by a rigid spherical body

We consider the fracture modes of circular metal plates on normal impact by a rigid spherical body, determine their dependence on the rigidity and plasticity characteristics of the plate material and on its boundary conditions and geometric dimensions referred to the ball diameter, and clarify how the fracture character changes as the impact point approaches the plate edge. For all variations in the collision conditions, we determine the value of the ballistic limit and construct the regions of possible estimation of its value under different, still unstudied experimental conditions.     

A Generalized Formulation of Elastodynamics: Small on Rigid

The conventional theory of linearized elastodynamics addresses the case of motions that have small displacement gradients with respect to a reference configuration of the elastic body that is unstressed and at rest. Here, we develop a theory of much wider applicability in which the linearization is with respect to a reference configuration that is in rigid motion. More specifically, with an eye toward application of the theory to analysis of the motions of relatively inflexible machine parts, we view the motion as being composed of a rigid motion, which corresponds to the applied loads and initial conditions for the body under consideration, and an infinitesimal motion, in which the displacement from the rigid motion has a small gradient.     

Stress singularities in an anisotropic body of revolution

To fill the gap in the literature on the application of three-dimensional elasticity theory to geometrically induced stress singularities, this work develops asymptotic solutions for Williams-type stress singularities in bodies of revolution that are made of rectilinearly anisotropic materials. The Cartesian coordinate system used to describe the material properties differs from the coordinate system used to describe the geometry of a body of revolution, so the problems under consideration are very complicated. The eigenfunction expansion approach is combined with a power series solution technique to find the asymptotic solutions by directly solving the three-dimensional equilibrium equations in terms of the displacement components. The correctness of the proposed solution is verified by convergence studies and by comparisons with results obtained using closed-form characteristic equations for an isotropic body of revolution and using the commercial finite element program ABAQUS for orthotropic bodies of revolution. Thereafter, the solution is employed to comprehensively examine the singularities of bodies of revolution with different geometries, made of a single material or bi-materials, under different boundary conditions.     

Multipolar continuum mechanics

A general theory of multipolar displacement and velocity fields with corresponding multipolar body and surface forces and multipolar stresses is developed using an energy principle, an entropy production inequality and invariance conditions under superposed rigid body motions. Constitutive equations for the multipolar stresses are discussed and explicit results are given for an elastic medium. Work in a previous paper by the present authors (1964) is shown to be a special case of that given here.     

Exact solutions for free vibration of transversely isotropic piezoelectric circular plates

By employing the general solution for coupled three-dimensional equations of a transversely isotropic piezoelectric body, this paper investigates the free vibration of a circular plate made of piezoelectric material. Three-dimensional exact solutions are then obtained under two specified boundary conditions, which can be used for both axisymmetric and non-axisymmetric cases. Numerical results are finally presented. The project supported by the National Natural Science Foundation of China (No. 19872060)