Non-reflecting boundary conditions

Uncertainties and dynamic problems of bolted joints and other fasteners

A survey of non-probabilistic uncertainty treatment in finite element analysis

It is 100 years since the well-know Mohr-Coulomb strength theory was established in 1900. A considerable amount of theoretical and experimental research on strength theory of materials under complex stress state was done in the 20th Century. This review article presents a survey of the advances in strength theory (yield criteria, failure criterion, etc) of materials (including matellic materials, rock, soil, concrete, ice, iron, polymers, energetic material, etc) under complex stress, discusses the relationship among various criteria, and gives a method of choosing a reasonable failure criterion for applications in research and engineering. Three series of strength theories, the unified yield criterion, the unified strength theory, and others are summarized. This review article contains 1163 references regarding the strength theories. This review also includes a biref discussion of the computational implementation of the strength theories and multi-axial fatigue.

Advances in strength theories for materials under complex stress state in the 20th Century

Mathematical models of elastic structures have become very sophisticated: given the crucial material properties (mass density and the several elastic moduli), computer-based techniques can be used to construct exotic finite element models. By contrast, the modeling of damping is usually very primitive, often consisting of no more than mere guesses at “modal damping factors.” The aim of this paper is to raise the modeling of viscoelastic structures to a level consistent with the modeling of elastic structures. Appropriate material properties are identified which permit the standard finite element formulations used for undamped structures to be extended to viscoelastic structures. Through the use of “dissipation” coordinates, the canonical “M , K ” form of the undamped motion equations is expanded to encompass viscoelastic damping. With this formulation finite element analysis can be used to model viscoelastic damping accurately.

Dynamics of viscoelastic structures: a time-domain finite element formulation

The finite element analysis of dynamic problems in an infinite, isotropic medium is examined. To simulate the physically infinite system by a finite model, an energy absorbing boundary is proposed. This boundary is frequency independent and proves to be very efficient in absorbing stress waves. The boundary constants are calculated for the particular cases of plane strain and axisymmetry for isotropic materials.

Unified Boundary for Finite Dynamic Models

Seismic cracking of concrete gravity dams by plastic-damage model using different damping mechanisms

One of the important factors that lead to errors in settlement predicitions is the degree of precision in obtaining the soil parameters. Most mathematical methods for reliability modelling offered to date in the area of geomechanics are based on the classical probabilistic approach, in which soil properties are treated as random variables. In this paper, a model based on the theory of fuzzy sets is presented to take account of the uncertainty in the soil behaviour. This proposed method considers the elastic modulus and Poisson's ratio as two fuzzy numbers in the elastic matrix. An example is given to show the possibility distributions of the displacements and the stresses at some locations in the soil medium. By means of a fuzzy inference scheme, the total possibility distributions or total membership functions of the finite element results may be obtained by considering the estimated error resulting from the mesh discretization.

Fuzzy finite element analysis of a foundation on an elastic soil medium

In this paper, an elastoplastic analysis based on fuzzy mathematics and using finite element method will be described. The Drucker–Prager yield criterion and the elasto-plastic matrix are fuzzified for the non-linear analyses which adopt the initial stress method for the solution. A numerical example is given to illustrate the possible variations in the displacements and the extent of plastic zones at the discrete membership functions. A reliability index of a membership grade based on the concept of non-probabilistic entropy is also proposed.

Elasto‐plastic finite element analysis with fuzzy parameters

A methodology to derive the membership function of a fuzzy set with objective and subjective information about a fuzzy event is introduced in this paper, This systematic framework makes use of the fuzzy calculus, the program-evaluation and review technique (PERQ, in operations research, and the outstanding concept of special relativity theory to transform these types of information into a fuzzy set with a resultant membership function. The subjective information can be the multi-inputs of expert knowledge. The objective part is the statistical data with their known probability-density function (pdf); however, this probability measure partly reflects the uncertainty assessment and is considered insufficient to describe an actual fuzzy event. If objective information is absent, this transforming or fuzzifving process can also be used to combine the different viewpoints of expertise.

Somasundaram Valliappan

Papers

Unified Boundary for Finite Dynamic Models

Seismic cracking of concrete gravity dams by plastic-damage model using different damping mechanisms

Fuzzy finite element analysis of a foundation on an elastic soil medium

Elasto‐plastic finite element analysis with fuzzy parameters

Constructing the Membership Function of a Fuzzy Set with Objective and Subjective Information