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Of course, an interest in meaning goes back much further in time than the period of modern linguistics. Some of the earliest recorded speculation about language concerned meaning: for instance, the ‘nature’ or ‘convention’ dispute among the Greeks—was there, they asked, something which made the word ‘cow’ the natural one to apply to that animal over there, or was it simply a matter of convention? And there has long been an interest in meaning among students of literature, philosophy, psychology, anthropology, and so on—as is only to be expected, since the main function of language is to convey some sort of meaning, whether we define this in a narrow way, or in a broader one, including connotation, emotion, and so on.

The purpose of this paper is to check the efficiency of isogeometric analysis (IGA) by comparing its results with classical finite element method (FEM), generalized finite element method (GFEM) and other enriched versions of FEM through numerical examples of free vibration problems.

Since its conception, IGA was widely applied in several problems. In this paper, IGA is applied for free vibration of elastic rods, beams and trusses. The results are compared with FEM, GFEM and the enriched methods, concerning frequency spectra and convergence rates.

The results show advantages of IGA over FEM and GFEM in the frequency error spectra, mostly in the higher frequencies.

Isogeometric analysis shows a feasible tool in structural analysis, with emphasis for problems that requires a high amount of vibration modes.

This study aims to present a new hybrid formulation based on non-uniform rational b-splines functions and enrichment strategies applied to free and forced vibration of straight bars and trusses.

Based on the idea of enrichment from generalized finite element method (GFEM)/extended finite element method (XFEM), an extended isogeometric formulation (partition of unity isogeometric analysis [PUIGA]) is conceived. By numerical examples the methods are tested and compared with isogeometric analysis, finite element method and GFEM in terms of convergence, error spectrum, conditioning and adaptivity capacity.

The results show a high convergence rate and accuracy for PUIGA and the advantage of input enrichment functions and material parameters on parametric space.

The enrichment strategies demonstrated considerable improvements in numerical solutions. The applications of computer-aided design mapped enrichments applied to structural dynamics are not known in the literature.

Various time integration methods and time finite element methods have been developed to obtain the responses of structural dynamic problems, but the accuracy and computational efficiency of them are sometimes not satisfactory. The purpose of this paper is to present a more accurate and efficient formulation on the basis of the weak form quadrature element method to solve linear structural dynamic problems.

A variational principle for linear structural dynamics, which is inspired by Noble's work, is proposed to develop the weak form temporal quadrature element formulation. With Lobatto quadrature rule and the differential quadrature analog, a system of linear equations is obtained to solve the responses at sampling time points simultaneously. Computation for multi-elements can be carried out by a time-marching technique, using the end point results of the last element as the initial conditions for the next.

The weak form temporal quadrature element formulation is conditionally stable. The relation between the normalized length of element and the suggested number of integration points in one element is given by a simple formula. Results show that the present formulation is much more accurate than other time integration methods and its dissipative property is also illustrated.

The weak form temporal quadrature element formulation provides a choice with high accuracy and efficiency for solution of linear structural dynamic problems.

We compare potential‐based (ø‐U‐P0) and displacement‐based finite element methods for static analysis of contained fluids. A general transient formulation may be specialized to static analysis in both cases. In the potential‐based method velocity potentials (ø) and a single pressure (P0) variable are the unknowns in the fluid region. Displacements are the unknowns in the fluid for displacement‐based methods. Higher‐order displace‐ment‐based elements may produce singular matrices for some static analyses, restricting us to four‐node elements for reliability. While both methods can yield excellent results when compared with experimental data, potential‐based methods appear to have computational advantages over displacement‐based methods.

The structural acoustic problem, wherein an acoustic domain is confined within a partly flexible laminated composite enclosure is presented. From the finite element free vibration analysis of the laminated folded plate structure a mobility relation is derived between the normal velocity of the structure and normal pressure on the structure. A boundary element solver for the Helmholtz equation with quadratic isoparametric elements is developed using pressure‐velocity formulation. Velocity is known over certain parts of the boundary, the rest being the interactive boundary, where the mobility relation correlates nodal pressures and velocities, neither explicitly known. The pressure boundary values are solved from the boundary element and the mobility relations, while the nodal particle velocities and domain pressures are computed at desired points thereafter. New results presented here reveal the effects of the variation in magnitude of structural damping, fiber angles and the thickness of walls.

Stiffened plates have been widely used in civil, marine, aerospace engineering. As a kind of thin-walled structure operating in complex environment, stiffened plates mostly undergo a variety of dynamic loads, which may sometimes result in large-amplitude vibration. Additionally, initial stresses and geometric imperfections are widespread in this type of structure. Furthermore, it is universally known that initial stresses and geometric imperfections may affect mechanical behavior of structures severely, particularly in dynamic analysis. Thus, the purpose of this paper is to study the stress variation rule of a stiffened plate during large-amplitude vibration considering initial stresses and geometric imperfections.

The initial stresses are represented in the form of initial bending moments applying to the stiffened plate, while the initial geometric imperfections are considered by means of trigonometric series, and they are assumed existing in the plate along the z-direction exclusively. Then, the dynamic equilibrium equations of the stiffened plate are established using Lagrange’s equation as well as aforementioned conditions. The nonlinear differential equations of motion are simplified as a two-degree-of-freedom system by considering 1:2 and 1:3 internal resonances, respectively, and the multiscale method is applied to solve the equations.

The influence of initial stresses on the plate, stresses during internal resonance is remarkable, while that is moderate for initial geometric imperfections. (Upon considering the existence of initial stresses or geometric imperfections, the stresses of motivated modes are less than the primary mode for both and internal resonances). The influence of bidirectional initial stresses on the plate’s stresses during internal resonance is more remarkable than that of unidirectional initial stresses. The coupled vibration in 1%3A2 internal resonance is fiercer than that in internal resonance.

Stiffened plates are widely used in engineering structures. However, as a type of thin-walled structure, stiffened plates vibrate with large amplitude in most cases owning to their complicated operation circumstance. In addition, stiffened plates usually contain initial stresses and geometric imperfections, which may result in the variation of their mechanical behavior, especially dynamical behavior. Based on the above consideration, this paper studies the nonlinear dynamical behavior of stiffened plates with initial stresses and geometrical imperfections under different internal resonances, which is the originality of this work. Furthermore, the research findings can provide references for engineering design and application.

The purpose of this paper is to present a numerical model to investigate the dynamic behavior and force coefficients of a compact squeeze film damper with dual film clearances adjusted by an elastic ring, known as elastic ring squeeze film damper (ERSFD).

The governing equations of ERSFD as well as the boundary conditions are obtained based on Reynolds equation. A simplified Greenwood–Williamson model is implemented to investigate the contact behavior between the elastic ring and the journal. The interactions between the films and the elastic ring are achieved by block iterative method.

The radial deformation as well as velocity of the elastic ring are captured to illustrate the pressure profiles of the inner and outer films. High-order frequency components related to the number of the boss N are observed on the frequency spectrum of the film force. The force coefficients of the ERSFD are constant for a wider range of non-dimensional whirling radius ε compared with conventional squeeze film damper.

The force coefficients of the ERSFD are obtained by assuming that the journal center moves in a circular centered orbit. High-order frequency components related to the number of bosses N are observed. These findings may provide helpful materials for the application of the ERSFD.

A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given. The bibliography at the end of the paper contains 1,726 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1996‐1999.

Distributed control is an effective method for controlling and suppressing excessive vibrations of continuous systems. Optimal distributed control for a plate problem is solved utilizing a maximum principle after the introduction of a quadratic index of performance in terms of displacement, velocity and a control force as well as an adjoint variable. The problem is reduced to solving a system of partial differential equations for the state variable and the adjoint variable subjected to boundary, initial and terminal conditions. A numerical algorithm is presented to solve the optimal distributed control problem in the space‐time domain which reduces the computational effort required to solve the initial‐terminal‐boundary value problem. Results obtained for a simply supported, rectangular, thin plate are also presented.