摘要:

Given a system of vectorial equilibrium equations for force and moment stress in a finitely deforming medium, we derive a system of force and moment strain‐displacement relations, consistent with the former via application of the principle of virtual work. We then obtain a system of vectorial compatibility equations, and we establish a connection between the present description of force stresses and strains, for the limiting case of absent moment stresses, with the classical description involving Kirchhoff stresses and Green strains, including the statement of constitutive equations corresponding to a given set of such equations for the measures of Kirchhoff and Gree

ISSN:0022-2526    

DOI:10.1002/sapm19755411

年代:1975

数据来源: WILEY

摘要:

Phase plane techniques are used to find finite amplitude solutions of a nonlinear second order boundary value problem. Each of these solutions represents a steady state of a model biochemical reaction proposed by Prigogine, in a limiting value of a parameter.

ISSN:0022-2526    

DOI:10.1002/sapm19755419

年代:1975

数据来源: WILEY

摘要:

An approach to a large scale network routing problem with nonlinear cost function is described, along with an example of its application. The approach to the problem involves a multistage construction process. This approach is applied to the telpaking problem. Results are obtained in applying this method to a 53 node sample problem.

ISSN:0022-2526    

DOI:10.1002/sapm197554117

年代:1975

数据来源: WILEY

摘要:

The inverse problem of the calculus of variations, i.e., the existence and formulation of variational principles for systems of nonlinear partial differential equations, is treated by application of a theorem due to Vainberg. Three types of principles are discussed: potential, alternate potential, and composite principles. Potential principles are those for which the equations, as written, admit a variational formulation. Alternate potential principles are those for which the equations admit a variational formulation only after a differential transformation of variables. Composite principles are those in which, in addition to the original variables, a set of adjoint variables is defined. A composite principle may always be formulated. Consistency relations for the existence of a potential are formulated for general systems of nonlinear partial differential equations of any order. These conditions are quite stringent and severely restrict the class of operators which admit a variational formulation. The results of the development are used to treat many well‐known equations in nonlinear wave mechanics. These include the Burgers, Korteweg‐deVries, and sine‐Gordon equations and evolution and model equations for interfacial waves. The Navier‐Stokes equations and the Boussinesq equations for an infinite Prandtl number fluid are briefly treated; these latter equations do not possess a potential pr

ISSN:0022-2526    

DOI:10.1002/sapm197554131

年代:1975

数据来源: WILEY

摘要:

The general theory for the slow dispersion of nonlinear wave trains, first studied by Whitham, is applied to a wave train, which, in the weakly nonlinear limit, exhibits resonant singularities. Numerical and perturbation methods are used to develop singly periodic solutions both away from and near all such critical values. Similarly, the equations governing the slow modulations of such a system are found by asymptotic analysis. The expansions are found to be valid so long as the wave train is sufficiently nonlinear. These ideas should be applicable to other problems where resonant singularities arise, in particular, multiphase modes.

ISSN:0022-2526    

DOI:10.1002/sapm197554161

年代:1975

数据来源: WILEY

摘要:

An inequality is derived for the Möbius function of a finite geometric latticeL. Equality is characterized by the modularity of certain elements ofL. Applications are given to other inequalities involving Whitney numbers, ordered bases, and maximal chains

ISSN:0022-2526    

DOI:10.1002/sapm197554171

年代:1975

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm197554175

年代:1975

数据来源: WILEY