Limit Design of Frames with Axial Force-Bending Moment Interaction

ABSTRACT

A method for optimum plastic design of plane frames is studied, taking into account the axial force-bending moment interaction plastic behavior. The frame is regarded as a discrete model, formed by rigid elements which are separated by (generalized) plastic hinges. Alternative loading conditions are considered, in addition to the action of the design-dependent self-weight. The optimization problem is solved as a problem of linear programming into which some technological and construction requirements are also introduced. Optimality conditions are also discussed.     

T -stress in piezoelectric solid

The non-singular and bounded terms for stresses near the crack tip were investigated. The crack problem in a transversely isotropic piezoelectric solid for the plane problem was dealt with. The principle of superpsition and the Plemelj formulation were introduced. The non-singular terms are given by solving Rieman-Hilbert problem. It is shown that the non-singular terms are influenced by the elastic and electric constants. Contributed by WANG Biao Foundation items: the Nature Science Foundation of Shandong of China (Q99F15); the Post Doctoral Science Foundation of Heilongjiang Provice of China Biography: MA Hao (1967≈), Professor, Doctor     

Asymptotic Stability of Riemann Solutions for a Class of Multidimensional Systems of Conservation Laws with Viscosity

We prove the asymptotic stability of two-state nonplanar Riemann solutions for a class of multidimensional hyperbolic systems of conservation laws when the initial data are perturbed and viscosity is added. The class considered here is those systems whose flux functions in different directions share a common complete system of Riemann invariants, the level surfaces of which are hyperplanes. In particular, we obtain the uniqueness of the self-similar L^∞ entropy solution of the two-state nonplanar Riemann problem. The asymptotic stability to which the main result refers is in the sense of the convergence as t→∞ in L_loc¹ of the space of directions ξ = x/t. That is, the solution u(t, x) of the perturbed problem satisfies u(t, tξ)→R(ξ) as t→∞, in L_loc¹(ℝⁿ), where R(ξ) is the self-similar entropy solution of the corresponding two-state nonplanar Riemann problem.     

ON THE WELL POSEDNESS OF INITIAL VALUE PROBLEM FOR EULER EQUATIONS OF INCOMPRESSIBLE INVISCID FLUID(Ⅰ)

The ill posed initial value problem of the Euler equations and the formal solvability of ill posed problem based on stratification theory are discussed. For some ill posed initial value problems, the existence conditions of formal solutions and the methods of how to construct a formal solution are given. Finally, an example is given to discuss the ill posedness of the initial value problem on hyper plane {t=0} in R⁴, and explain that the problem has more than one solution. Foundation item: the National Natural Science Foundation of China (19971054) Biography: Shen Zhen (1977−)     

Note on the Radial Deformation and Stresses in Anisotropic Nonhomogeneous Elastic Media

Abstract

In this paper we study the elasticity problem of a cylindrically anisotropic, elastic medium bounded by two axisymmetric cylindrical surfaces subjected to normal piessures (plane strain). The material of the structure is orthotropic with cylindrical anisotropy and, in addition, is continuously inhomogeneous with mechanical properties varying along the radius. General solutions in terms of Whittaker functions are presented. The results obtained by St. Venant for a homogeneous cylindrically anisotropic medium can be deduced from the general solutions. The problem of a solid cylinder of the same medium under the external pressure is also solved as a particular case of the above problem. Problems of the type covered in this paper are encountered in nuclear reactor design.     

On Large-Time Behavior of Solutions to the Compressible Navier-Stokes Equations in the Half Space in R 3

 The Navier-Stokes equation for compressible viscous fluid is considered on the half space in R ³ under the zero-Dirichlet boundary condition for the momentum with initial data near an arbitrarily given equilibrium of positive constant density and zero momentum. Time decay properties in L ² norms for solutions of the linearized problem are investigated to obtain the rate of convergence in L ² norms of solutions to the equilibrium when initial data are sufficiently close to the equilibrium in . Some lower bounds are derived for solutions to the linearized problem, one of which indicates a nonlinear phenomenon not appearing in the case of the Cauchy problem on the whole space. (Accepted May 8, 2002) Published online October 18, 2002 Communicated by T.-P. LIU     

On the (u, p) problem in the theory of elasticity

A problem of the theory of elasticity is considered for a body with vectors of displacements u and loads p simultaneously defined on one part of the body and with undefined conditions on the remaining part of the body. For a doubly connected domain, where the vectors u and p are set on one of its boundaries (inner or outer), an iterative method based on reduction of the initial problem to a sequence of mixed problems is justified. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 100–103, May–June, 2006.     

On the Problem of Torsion in Finite Elasticity:Part I,The General Formulation in the Case of Torsion with Variable Twist

ABSTRACT

The problem of nonuniform torsion of beams with solid cross-sections is examined in the finite displacement theory of elasticity. Two approximate theories are formulated by applying Reissner's theorem for finite elastic deformations. A perturbation solution scheme is presented, to study results implied by the two approximate formulations.     

On Optimality Conditions for Trusses with Nonuniform Stress Constraints*

ABSTRACT

The optimal design of a truss subjected to a single loading system and stress constraints, which are not necessarily the same in each bar, is considered. Sufficient conditions for global optimality are derived by variational methods. While these optimality criteria lead to a linear programming formulation of the problem, they show in a clear physical way how the optimal design is found, and that advantages accrue from incorporating the optimality criteria in a numerical scheme.     

A Compact Linear Programming Procedure for Optimal Design in Plane Stress∗

Abstract

Two-dimensional problems in plane stress are considered, with a view toward obtaining the optimal distribution of thickness under the condition that there be no collapse. Geometrical constraints on the shape of the structure are included for the purpose of meeting practical limitations.

The aim of the paper is to give a new theoretical formulation to the problem in order to effect greater savings in computer time. In particular, the number of constraints is shown to be significantly reduced, and static admissibility is guaranteed even when dealing with a reduced formulation of the problem. This is done by linearizing the yield surface and by expressing the stress vectors as linear nonnegative combinations of the vertices of the yield polyhedron, and by enforcing plastic conformity in a simple compact way.

Known static and kinematic formulations are rederived by invoking the properties of linear programming. The effectiveness of the procedure is demonstrated through applications at the end of the paper.     

ANALYSIS/DESIGN CALCULATIONS OF TRANSONIC FLOWS

SUMMARY

Analysis/design calculations of transonic flow are discussed and several improvements are made. The nonisentropic potential method is used to calculate the inviscid transonic flow analysis problem instead of the traditional potential method. An inverse integral 3D boundary layer method is used to calculate the boundary layer in the viscous transonic flow analysis problem. The viscous/inviscid interaction calculations are carried out by a semi-inverse coupling scheme. In design problem calculations, an improved residual-correction method is used. Three individual methods are combined in a global algorithm and computing code. The improvements speed up the convergence, increase applicability and computational efficiency. Some numerical results are given to illustrate that the present method provides an effective engineering tool of high accuracy and efficiency in three dimensional transonic analysis and design situations.     

Analysis of Tracked-Vehicle Suspension Systems Using a Frictional Contact Problem Formulation

ABSTRACT

A new procedure for analysis of tracked-vehicle suspension systems under a track length constraint, based on a frictional contact problem formulation, is presented. Impenetrability, inextensibility, unilateral behavior of track, and friction conditions are expressed in complementarity form. The resulting problem is then amenable to efficient numerical algorithms, such as the modified simplex method. This approach is demonstrated through numerical applications to a model of a tracked-vehicle suspension system.     

On Optimal Shell Prestressing

Abstract

The problem of optimum selection and distribution of prestressing forces in a shell structure subjected to different loads is solved within membrane theory. The range of admissible prestressing tensors at a shell point is deter mined and the selection of optimum prestressing is described. The problem is discretized, linearized, and reduced to that of linear mathematical programming. A method of tracing cable trajectories is given. Graph theory approach is applied to form design combinations of elementary loads when these are related by logical conditions. An outline is given of the computation of a prestressed secondary containment of a nuclear reactor.     

饱和两相介质动力固结问题时域求解的精细时程积分方法

针对u-p形式的饱和两相介质波动方程,采用精细时程积分方法计算固相位移u,采用向后差分算法求解流体压力p,建立了饱和两相介质动力固结问题时域求解的精细时程积分方法。针对标准算例,对该方法的计算精度进行了校核。开展了该方法相关算法特性的研究,对采用不同数值积分方法计算非齐次波动方程特解项计算精度的差异进行了对比研究,并对采用不同积分点数目的高斯积分法计算特解项条件下计算精度的差异进行了对比研究。研究结果表明,(1)该方法具有良好的计算精度。(2)计算非齐次波动方程特解项的数值积分方法中,梯形积分法的计算精度最差,高斯积分法、辛普生积分法和科茨积分法都具有较好的计算精度。(3)增加高斯积分点数目对于提高计算精度的作用并不显著。     

Scattering of harmonic antiplane shear waves by an arc-shaped interfacial crack in functionally graded annular bi-material guide rail

Abstract

The dynamic behavior of an arc-shaped interfacial crack in an orthotropic functionally graded annular bi-material structure is investigated. In order for the analysis to be executable, the material properties are assumed to vary with the power function of the radial coordinates. By applying the separation variable method, the boundary value problem of the partial differential equation describing the fracture problem of this article can be transformed into a Cauchy kernel singular integral equation with the unknown jump of displacements across the crack surfaces. The obtained integral equation is solved numerically by Lobatto–Chebyshev collocation method to show the effects of the geometric and physical parameters upon the dynamic stress field near the crack tips.

Communicated by Kuang-Hua Chang.     

Stress analysis for an infinite strip weakned by periodic cracks

Stress analysis for an infinite stripcracks were assumed in a horizontal position,weakened by periodic cracks is studied. The and the strip was applied by tension “p“ in y-direction. The boundary value problem can be reduced into a complex mixed one. It is found that the EEVM ( eigenfunction expansion variational method) is efficient to solve the problem. The stress intensity factor at the crack tip and the T-stress were evaluated. From the deformation response under tension the cracked strip can be equivalent to an orthotropic strip without cracks. The elastic properties in the equivalent orthotropic strip were also investigated. Finally, numerical examples and results were given.     

Simulation of Initially Slackened and Stiffened Structures by Virtual Distortions∗

ABSTRACT

Variational principles and computational methods for analysis of initially slackened and stiffened structures are discussed. The simulation of clearances or internal dry fraction in structural elements by virtual (eigen) distortions is applied. Considerations presented are used in the problem of nonstandard design of structural settings, with clearances or friction in the structural joints, for load capacity maximization.     

An Energy Method Applied to Large Elastic Deflection of a Thin Plate of Bimodulus Material

Abstract

Some composite materials and high-polymers are known to behave differently in simple tension and compression under static loads. The present paper is concerned with a method of analysis of the bending of bimodulus elastic plates employing Ambartsumyan-Khachatryan's model for isotropic bimodulus materials. This problem may be reduced to the conventional problem of minimizing the potential energy of the plate as a whole. A simply supported thin square plate subjected to lateral load is analyzed numerically by a simplex method. Results of the calculation show that the effect of the difference between the tensile and compressive elastic moduli on the deformation of the plate may be substantial     

Symmetry-breaking at non-positive solutions of semilinear elliptic equations

We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semilinear elliptic equations on a ball with Dirichlet boundary conditions. For nonlinearities which are asymptotically affine linear, we find solutions at which the symmetry breaks. The kernel of the linearized equation at these solutions is an absolutely irreducible representation of the group O(n). For this kind of equation a transversality condition is satisfied if the perturbation of the affine linear problem is small enough. Thus we obtain, by the equivariant branching lemma, a large variety of isotropy subgroups of O(n) which occur as symmetries of the bifurcating solution branches.