Constraint manifolds for isotropic solids

Communicated by M. E. Gurtin     

Bifurcation sets and catastrophes in manifolds of steady states of pneumatic-tired machines under constant mechanical loads

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 3, pp. 89–95, March, 1995.     

Gradient vector fields with pulse action on manifolds

We consider gradient vector fields with pulse (smooth and continuous) action defined on a smooth compact manifold. In the course of investigation of the qualitative behavior of integral curves of these vector fields, we prove a criterion for the existence of closed orbits and a condition for their orbital stability. Translated from Neliniini Kolyvannya, Vol. 12, No. 1, pp. 134–144, January–March, 2009.     

Constraint groups

The complete list of constraint manifolds having the group structure is given.     

On deformations with constant modified stretches

Two plane, non-homogeneous, non-conformal deformations with constant modified stretches (the inflation of a circular cylindrical tube and the bending of a rectangular block into a sector of a circular tube) are shown to be possible in the absence of body forces in isotropic elastic solids that satisfy both the classical pressure-compression inequality and the Baker-Ericksen inequality.     

Regularity of invariant manifolds

Under mild conditions it is proved that an invariant submanifold ofX 0<1 for the equationdx/dt+Ax=f(x), A sectorial,fC'(X ,X),0<1, is a submanifold ofX ¹ as well. In addition, conditions are given for the semiflow of the equation to extend fromX toX and a new inertial manifold theorem is proved for the scalar reaction diffusion equation.     

CONSTRAINT VIOLATION STABILIZATION OF EULER-LAGRANGE EQUATIONS WITH NON-HOLONOMIC CONSTRAINTS

Two constraint violation stabilization methods are presented to solve the Euler Lagrange equations of motion of a multibody system with nonholonomic constraints. Compared to the previous works, the newly devised methods can deal with more complicated problems such as those with nonholonomic constraints or redundant constraints, and save the computation time. Finally a numerical simulation of a multibody system is conducted by using the methods given in this paper.     

Supersonic ejectors with mixing at constant cross-section

Summary Based upon the already classical concept of a mixing process divided into an expansion- and a mixing region, a simple integral theory was developed in part I.In this part is described an extensive experimental investigation in which the parameters are varied over a large range; e.g. it is found that a large primary after-expansion can be allowed provided the mixing tube is convergent in the region of expansion. Furthermore it is shown that the theory offers an explanation for the essential experimental phenomena; quantitatively corrections are necessary in points with a complex flow structure.Some general directions are given for the optimum design of an ejector.     

Algorithms for motions with constant stretch history

Summary Necessary and sufficient conditions to establish that a velocity field gives rise to a motion with constant stretch history are developed and illustrated with a number of examples. Extensions to determine whether a given strain history is of the above type is also made.

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Zusammenfassung Es werden notwendige und hinreichende Kriterien dafür entwickelt, daß ein Geschwindigkeitsfeld eine Bewegung mit konstanter Deformationsvorgeschichte (MWCSH) erzeugt, und diese Kriterien werden an einer Anzahl von Beispielen veranschaulicht. Ebenso werden Erweiterungen angegeben, mit Hilfe derer man bestimmen kann, ob eine vorgegebene Deformationsvorgeschichte vom vorgenannten Typ ist.

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With 2 figures     

Quasivariational Solutions for First Order Quasilinear Equations with Gradient Constraint

We prove the existence of solutions for a quasi-variational inequality of evolution with a first order quasilinear operator and a variable convex set which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself. The only required assumption on the nonlinearity of this constraint is its continuity and positivity. The method relies on an appropriate parabolic regularization and suitable a priori estimates. We also obtain the existence of stationary solutions by studying the asymptotic behaviour in time. In the variational case, corresponding to a constraint independent of the solution, we also give uniqueness results.     

具有Homologous变形约束立体桁架的形态分析

本文研究了具有Homologous位移约束的结构形状分析问题。文中第一部分把结点分成三类:表示Homologous变形点(自由度=h),形状可变点(自由度=f)和边界点。然后对于任意的桁架结构给出Homologous参数,n=h+f和m=1+f,引入具有n×m的系数矩阵的基础方程。在第二部分,利用广义逆矩阵导出基础方程的解存在条件。然后建立包含未知结点坐标的非线性方程组,并由Newton-Raphson法进行数值分析,以找出最终形状。最后一部分举了一个三维桁架的例子,以说明该方法的有效性,实用性。     

New Bifurcation Patterns in Elementary Bifurcation Problems with Single-Side Constraint

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LAGRANGIAN MECHANICS ON KAHLER MANIFOLDS

IntroductionLagrangian mechanics is an important part of analytical mechanics.It was establishedby J.Lagrange by means of the Euclidean analytical geometry and calculus in his famouswork“Analytical Mechanics”in1788.Now,itwas established in Riemann manif…     

Parameter identification in a soil with constant diffusivity

We consider infiltration into a soil that is assumed to have hydraulic conductivity of the form K = K = K_se^h and water content of the form = K – _r. Here h denotes capillary pressure head while K_s, , and _r represent soil specific parameters. These assumptions linearize the flow equation and permit a closed form solution that displays the roles of all the parameters appearing in the hydraulic function K and . We assume K_s and _r to be known. A measurement of diffusivity fixes the product of and resulting in a parameter identification problem for one parameter. We show that this parameter identification problem, in some cases, has a unique solution. We also show that, in some cases, this parameter identification problem can have multiple solutions, or no solution. In addition it is shown that solutions to the parameter identification problem can be very sensitive to small changes in the problem data.     

Snap-through under unilateral displacement control with constant velocity

When the side of a beverage can or the domed lid of a jar is pushed inward, all or part of the structure may suddenly snap into an inverted configuration. The velocity of the pushing motion affects this instability. Most previous analyses of snap-through have considered force control (increasing the pushing force, e.g., a weight). Snap-through under dynamic, unilateral displacement control is investigated here, with the indentor moving at constant velocity (as in a universal testing machine) until snap-through occurs. Shallow elastic arches with immovable pinned ends are analyzed. Attention is focused on the critical height of the indentor at which snap-through is initiated. The effects of the indentor velocity, indentor location along the span, initial arch height, and damping magnitude are investigated. In addition, experiments are conducted on shallow buckled beams, which behave similarly to arches. Usually, the higher the indentor velocity, the further the indentor must move before snap-through occurs.