p-version finite elements and finite cells for finite strain elastoplastic problems

In this paper, the p-version finite element method and its fictitious domain extension, the finite cell method, are extended to the finite strain J₂ plasticity. High-order shape functions are used for the finite element approximation of volume-preserving plastic dominated deformations. The accuracy and efficiency of p-version elements and cells in the finite plastic strain range are evaluated by the computation of two benchmark problems. It is shown that they provide locking free behavior and simplified meshing. These results are verified in comparison with the results of h-version elements in F-bar formulation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Residually finite, congruence meet-semidistributive varieties of finite type have a finite residual bound

We show that a residually finite, congruence meet-semidistributive variety of finite type is residually for some finite . This solves Pixley's problem and a special case of the restricted Quackenbush problem.

     

Representations of finite universal algebras in finite semigroups

An answer is given to the question of what conditions must be imposed on a signature in order that every finite algebra with this signature can be represented in the Mal'tsev-Cohn sense in a finite semigroup.Translated from Matematicheskie Zametki, Vol. 9, No. 3, pp. 285–290, March, 1971.The author wishes to thank A. G. Kurosh and Yu. K. Rebane for directing this work.     

Dual-standard subgroups of finite and locally finite groups

A subgroup D of a group G is called dual-standard if, for all subgroups X and Y of G, <XχD,YχD>=<X,Y>χD. When G is finite, Zappa has given some information concerning the way in which D is embedded in G and the structure of G itself. Among other things, Zappa makes reference to the maximal normal Hall subgroup L of G contained in D. In general L can be arbitrary. The main result of this work, however, is to show that the commutator of L with a complement in G is nilpotent.     

Nonlinear,finite deformation,finite element analysis

The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli (C^e) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated with energy conservation and work-conjugacy due to the use of the Jaumann objective stress rate in ABAQUS nonlinear incremental analysis is viewed as a consequence of the implementation of a constitutive model that violates these requirements.     

On residually finite groups of finite general rank

Following A. I.Mal’tsev, we say that a group G has finite general rank if there is a positive integer r such that every finite set of elements of G is contained in some r-generated subgroup. Several known theorems concerning finitely generated residually finite groups are generalized here to the case of residually finite groups of finite general rank. For example, it is proved that the families of all finite homomorphic images of a residually finite group of finite general rank and of the quotient of the group by a nonidentity normal subgroup are different. Special cases of this result are a similar result of Moldavanskii on finitely generated residually finite groups and the following assertion: every residually finite group of finite general rank is Hopfian. This assertion generalizes a similarMal’tsev result on the Hopf property of every finitely generated residually finite group.     

Groups acting on finite dimensional spaces with finite stabilizers

It is shown that every H -group G of type admits a finite dimensional G-CW-complex X with finite stabilizers and with the additional property that for each finite subgroup H, the fixed point subspace X ^H is contractible. This establishes conjecture (5.1.2) of [9]. The construction of X involves joining a family of spaces parametrized by the poset of non-trivial finite subgroups of G and ultimately relies on the theorem of Cornick and Kropholler that if M is a -module which is projective as a -module for all finite then M has finite projective dimension. Received: April 30, 1997     

Sojourn times with finite time-horizon in finite semi-markov processes

Let Y = {Y_t:t ≥ 0} be a semi-Markov process with finite state space S. Assume that Y is either irreducible and S is then partitioned into two classes A and B, or, that Y is absorbing and S is partitioned into A, B and C, where C is the set of all absorbing states of Y. Denote by T_{A, m}(t) the mth sojourn time of Y in A during [0, t]. T_{A, m}(t) is thus defined as the duration in [0, t] of the mth visit of Y to A if A is visited by Y during [0, t] at least m times; T_{A, m}(t) = 0 otherwise. We derive a recurrence relation for the vectors of double Laplace transforms g_m**(T₁,T₂) = {g_m**(T₁, T₂;S):sSC}, m = 1,2,… which are defined by with T₁, T₂, Re(T₁), Re(T₂) > 0. This result is then applied to alternating renewal processes. Symbolic Laplace transform inversion with MAPLE is used to obtain the first two moments of T_{A, m}(t). The assumed holding time distributions are exponential and Erlang respectively. This paper is a continuation of some of the author's recent work on the distribution theory of sojourn times in a subset of the finite state space of a (semi-)Markov process where the time horizon t = + ∞. The practical importance of considering a finite time horizon for semi-Markov reliability models has been discussed recently by Jack (1991), Jack and Dagpunar (1992), and Christer and Jack (1991).     

Conjugate biprimitive finite groups saturated with finite simple subgroups

A group G is saturated with groups of the set X if every finite subgroup K≤G is embedded in G into a subgroup L isomorphic to some group of X. We study periodic biprimitive finite groups saturated with groups of the sets {L₂(pⁿ)}, {Re(3²ⁿ⁺¹)}, and {Sz(2²ⁿ⁺¹)}. It is proved thai such groups are all isomorphic to {L₂(P)}, {Re(Q)}, or {Sr(Q)} over locally finite fields. Supported by the RF State Committee of Higher Education. Translated fromAlgebra i Logika, Vol. 37, No. 2, pp. 224–245, March–April, 1998.     

Centralizers of finite nilpotent subgroups in locally finite groups

We investigate the structure of locally finite groups with a finite subgroup whose centralizer is close to a linear group. Deceased. Translated fromAlgebra i Logika, Vol. 35 No. 4, pp. 389–410, July–August, 1996.     

On finite and totally finite elements in vector lattices

, X , , , M l- M X , ( M) M .     

On finite unions and finite products with the D-property

We show that the product of a subparacompact C-scattered space and a Lindelöf D-space is D. In addition, we show that every regular locally D-space which is the union of a finite collection of subparacompact spaces and metacompact spaces has the D-property. Also, we extend this result from the class of locally D-spaces to the wider class of D-scattered spaces. All the results are shown in a direct way.