摘要:

Two classes of exact solutions are derived for the equations of three dimensional linear orthotropic elasticity theory governing flat (plate) bodies in plane strain or axisymmetric deformations. One of these is the analogue of the Lévy solution for plane strain deformations of isotropic plates and is designated as theinteriorsolutions. The other complementary class correspond to the Papkovich‐Fadle Eigenfunction solutions for isotropic rectangular strips and is designated as theresidualsolutions. For sufficiently thin plates, the latter exhibits rapid exponential decay away from the plate edges. A set of first integrals of the elasticity equations is also derived. These first integrals are then transformed into a set of exact necessary conditions for the elastostatic state of the body to be aresidualstate. The results effectively remove the asymptoticity restriction of rapid exponential decay of the residual state inherent in the corresponding necessary conditions for isotropic plate problems. The requirement of rapid exponential decay effectively limits their applicability to thin plates. The result of the present paper extend the known results to thick plate problems and to orthotropic plate problems. They enable us to formulate the correct edge conditions for two‐dimensional orthotropic thick plate theories with stress or mixed edge

ISSN:0022-2526    

DOI:10.1002/sapm198879293

年代:1988

数据来源: WILEY

摘要:

Lett= (t1,…,tn) be a point of ℝn. We shall write . We put, by the definition,Wα(u,m) = (m−2u)(α −n)/4[π(n− 2)/22(α +n− 2)/2Г(α/2)]J(α −n)/2(m2u)1/2; here α is a complex parameter,ma real nonnegative number, andnthe dimension of the space.Wα(u,m), which is an ordinary function if Re α ≥n, is an entire distributional function of α. First we evaluate {□ +m2}Wα + 2(u,m) =Wα(u,m), where {□ +m2} is the ultrahyperbolic operator. Then we expressWα(u,m) as a linear combination ofRα(u) of differntial orders;Rα(u) is Marcel Riesz's ultrahyperbolic kernel. We also obtain the following results:W−2k(u,m) = {□ +m2}kδ,k= 0, 1,…;W0(u,m) = δ; and {□ +m2}kW2k(u,m) = δ. Finally we prove thatWα(u,m= 0) =Rα(u). Several of these results, in the particular case µ = 1, wer

ISSN:0022-2526    

DOI:10.1002/sapm1988792127

年代:1988

数据来源: WILEY

摘要:

The properties of the solutions of the differential equationy″ =y2−x2−csubject to the condition thatyis bounded for all finitexdiscussed. The arguments of Holmes and Spence have been used by Ockendon, Ockendon, and Johnson to show that there are no solutions ifcis large and negative. Numerically we find that solutions exist providedcis greater than a critical valuec* and estimate this value to bec* = −…. Asxtends to + ∞ the solutions are asymptotic to . The relation betweenA+andϕ+are found analytically asA+→ ∞. This problem arises as a connection problem in the theory of resonant oscillation

ISSN:0022-2526    

DOI:10.1002/sapm1988792143

年代:1988

数据来源: WILEY

摘要:

A model consisting of two nonlinear coupled parabolic equations governing the combustion of a material is considered. Under certain assumptions, the concentration of the combustible material is shown to be largely spatially homogeneous. Construction of upper and lower solutions for the equation governing the temperature is then given in terms of the solution of an associated ordinary integrodifferential equation. Estimates for the critical parameters for the three type‐A geometries are obtaine

ISSN:0022-2526    

DOI:10.1002/sapm1988792159

年代:1988

数据来源: WILEY

摘要:

Cellular automata that exhibit soliton behavior are studied. A simple rule—the fast‐rule theorem (FRT)—is introduced, which allows immediate calculation of the evolution process. The FRT is suitable for the development of parallel algorithms, for the analysis and prediction of the behavior of the automata, and for hand calculation as well. The FRT consists of first selecting a finite set of sites and then obtaining the next state by simply inverting one bit in these sites, while leaving the remaining bits unchanged. This finite set can be detected by inspection. The distinction between single and multiple particles is made precise and shown to depend not only on the number of consecutive zeros separating particles but also on their position relative to the sites in the finite set mentioned above. Three applications are given. The first is a demonstration of the FRT as an analytical tool and settles the (up to now) open question of stability. The other two applications demonstrate the use of the FRT in the construction of a periodic particle and in obtaining soliton collisions by hand calcula

ISSN:0022-2526    

DOI:10.1002/sapm1988792173

年代:1988

数据来源: WILEY