While the study of psychology has offered little in the way of explaining the creative process, Koestler examines the idea that we are at our most creative when rational thought is suspended--for example, in dreams and trancelike states. All who read The Act of Creation will find it a compelling and illuminating book.

The Act of Creation

A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS

The status and some recent developments in computational modeling of flexible multibody systems are summarized. Discussion focuses on a number of aspects of flexible multibody dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental studies. The characteristics of the three types of reference frames used in modeling flexible multibody systems, namely, floating frame, corotational frame, and inertial frame, are compared. Future directions of research are identified. These include new applications such as micro- and nano-mechanical systems; techniques and strategies for increasing the fidelity and computational efficiency of the models; and tools that can improve the design process of flexible multibody systems. This review article cites 877 references. @DOI: 10.1115/1.1590354#

https://hosting.umons.ac.be/html/mecara/grasmech/PaperWasfyNoor.pdf

Computational strategies for flexible multibody systems

We survey some recent applications of radial basis functions (rbfs) for the BEM and related algorithms such as the method of fundamental solutions. Among these are the use of alternatives to the traditional 1+ r function in the dual reciprocity method such as thin plate splines, multquadrics and the recently discovered compactly supported positive definite rbfs, and convergence proofs of the DRM for Poisson’s equation. Newly discovered particular solutions for Helmholtz-type operators are discussed and applied to give efficient mesh free algorithms for the diffusion equation. In addition, a number of proposals are given for future applications of rbfs such as the use of surface rbfs for interpolation and the solution of boundary integral equations and the application of Kansa’s method to develop new rbf based coupled domain-boundary approximation methods.

Some recent results and proposals for the use of radial basis functions in the BEM

Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams are studied through a finite element approach. The exact shape functions for uniform homogeneous Timoshenko beam elements are used to formulate the proposed element. The accuracy of the present element is considerably improved by considering the exact variations of cross-sectional profile and mechanical properties in the evaluation of the structural matrices. Carrying out several numerical examples, the convergence of the method is verified and the effects of taper ratio, elastic constraint, attached mass and the material non-homogeneity on the natural frequencies and critical buckling load are investigated.

Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions

Finite Element Analysis Of An Axially Moving Beam, Part I: Time Integration

Vibration analysis of timoshenko beams with non-homogeneity and varying cross-section

A structural optimization algorithm is developed to minimize the weight of structures with truss and beam-type members under single- or multiple-frequency constraints. The cross-sectional areas of the structural members are considered as the design variables. The algorithm proposed combines the finite element technique based on the integrated force method with the mathematical programming technique. The equilibrium matrix is generated automatically using the finite element analysis, and the compatibility matrix is obtained directly using the displacement-deformation relations and the single value decomposition technique. When combining the equilibrium and the compatibility matrices with the force-displacement relations, the frequency eigenvalue equations are obtained with element forces as variables. Three structures, composed of truss and frame-type members, are studied to illustrate the procedure, and the results are compared with the literature. It is shown that, in structural problems with multiple frequency constraints, the analysis procedure (force or displacement method) significantly affects the final optimum design. The structural optimization based on the force method results in a lighter design. The proposed structural optimization method is efficient to analyze and optimize both truss and beam-type structures.

B. Tabarrok

Papers

Finite Element Analysis Of An Axially Moving Beam, Part I: Time Integration

Vibration analysis of timoshenko beams with non-homogeneity and varying cross-section

Structural optimization with frequency constraints using the finite element force method

Finite Element Analysis Of An Axially Moving Beam, Part II: Stability Analysis

Finite element formulation of a tapered Timoshenko beam for free lateral vibration analysis