Hidenori Murakami

A High-Order Laminated Plate Theory with Improved In-Plane Responses.

In order to improve the accuracy of the in-plane responses of the shear deformable laminated composite plate theories, a new high-order laminated plate theory was developed based upon Reissner’s new mixed variational principle [Int. J. Num. Meth. Eng.20, 1366 (1984)]. To this end, a zig-zag shaped C0 function and Legendre polynomials were introduced into the approximate in-plane displacement distributions across the plate thickness. The accuracy of the present theory was examined by applying it to the cylindrical bending problem of laminated plates which had been solved exactly by Pagano [J. Comp. Mat.3, 398 (1969)]. A comparison with the exact solutions obtained for several symmetric and asymmetric cross-ply laminates indicates that the present theory accurately estimates in-plane responses, even for small span-to-thickness ratios.

Static and dynamic analyses of tensegrity structures. Part 1. Nonlinear equations of motion

Abstract In order to present basic equations for static and dynamic analyses of a class of truss structures called tensegrity structures, large-deformation kinematics and kinetics were presented in both Eulerian and Lagrangian formulations. The two sets of equations of motion yield the same values even if different stress and strain measures were employed for their computation. The Eulerian formulation was implemented in an updated Lagrangian finite element code using Newton’s method with consistently linearized equations of motion. By utilizing the linearized Lagrangian equations of motion at pre-stressed initial configurations, harmonic modal analyses of a three-bar tensegrity module and a six-stage tensegrity beam were conducted. In the second part of the paper, linearized equations were utilized to investigate the equilibrium configurations of basic tensegrity modules and the stiffness of pre-stressed tensegirty structures.

Reduced nerve blood flow in edematous neuropathies: A biomechanical mechanism

Reduced nerve blood flow has been reported in two experimental neuropathies in which edema is an early and significant finding. While the mechanisms of fluid accumulation differed, both resulted in increases of endoneurial fluid pressure up to five times the normal value. As increased endoneurial fluid distends the nerve, the perineurial sheath resists expansion and endoneurial fluid pressure increases. The semirigid perineurium is also a conduit for regional nutritive vessels which provide the greater part of peripheral nerve blood flow. Engineering structural analysis of blood vessels entering the endoneurium suggests that moderate elevations in endoneurial fluid pressure can deform cylindrical vessels in the perineurium into elliptical shapes by creating circumferential elongation and longitudinal compression of the vessels which reduce the cross-sectional area of the lumen. We propose that the pathogenesis of reduced nerve blood flow in edematous neuropathies is linked to the unique structure of the peripheral nerve perineurium and the nerve vasculature, in particular to deformation of anastomotic vessels traversing it.

Static and dynamic analyses of tensegrity structures. Part II. Quasi-static analysis

Linearized Lagrangian equations developed in the first part of the paper were employed for static analyses of cyclic cylindrical tensegrity modules. Linearized equilibrium equations at natural configurations were used to investigate initial shape, static and kinematic indeterminancy, pre-stress and infinitesimal mechanism modes, and the sensitivity analysis of initial geometry. Linearized equilibrium equations at pre-stressed initial configurations were utilized to investigate pre-stress stiffening and to distinguish first-order mechanisms from higher-order mechanisms. To estimate critical loads for bar buckling and cable slacking, nonlinear equilibrium equations were employed to compute element forces. Further, the equivalence between the twist angle theorem obtained from a geometrical consideration and the equilibrium analysis was established for cyclic cylindrical tensegrity modules. It is concluded that infinitesimal mechanism modes and pre-stresses characterize the static and dynamic response of tensegrity structures.

Static and dynamic characterization of regular truncated icosahedral and dodecahedral tensegrity modules

Static and dynamic properties of a pair of dual spherical tensegrity modules invented by Buckminster Fuller are investigated. They are regular truncated icosahedral and dodecahedral tensegrity modules. The computation of the Maxwell number and the use of Calladines relation reveal that regular truncated icosahedral and dodecahedral tensegrity modules possess 55 infinitesimal mechanism modes. A reduced equilibrium matrix is presented for the initial shape finding to economically impose the existence of a pre-stress mode. Both the initial shape and the corresponding pre-stress mode are analytically obtained by using graphs of the icosahedral group and the reduced equilibrium matrix. For both icosahedral and dodecahedral modules the maximum values of the cable tension is always less than the absolute value of bar compression. In order to classify a large number of infinitesimal mechanism modes, modal analyses are conducted. Infinitesimal mechanism modes have the stiffness due to pre-stress and are associated with lowest natural frequencies. Their natural frequencies increase proportionally to the square root of the amplitude of pre-stress. It is found that there are only 15 distinct natural frequencies associated with the infinitesimal mechanism modes.

A second-order numerical scheme for integrating the endochronic plasticity equations

Abstract An efficient second-order numerical scheme is developed for integrating the endochronic plasticity equations of plastically incompressible solids, such as metals, for example. The numerical scheme is appropriate for use with finite element wave propagation codes based upon explicit time integration. Second-order accuracy is achieved by using Richardson extrapolation in connection with explicit integration of the governing equations. It is shown that Richardson extrapolation leads to more than an order of magnitude increase in computing speed over the usual approach, for comparable accuracy.

Initial shape finding and modal analyses of cyclic right-cylindrical tensegrity modules

Initial equilibrium and modal analyses of cyclic right-cylindrical tensegrity modules with an arbitrary number of stages are presented. There are m (⩾3) bars at each stage. The Maxwell number of the modules is 6−2m and is independent of the number of stages in the axial direction. Calladine’s relation reveals that there are 2m−5 infinitesimal mechanism modes. For multi-stage modules the necessary conditions for axial assembly of one-stage interior modules with the same internal element forces are investigated. One-stage modules with either congruent right-cylindrical modules or geometrically similar cone-shaped modules satisfy the necessary conditions. In this paper, the axial assembly of right-cylindrical modules with flip or quasi-flip symmetry is considered. For pre-stressed configurations, modal analyses are conducted to investigate the mode shapes of infinitesimal mechanism modes.

A mixture theory with a director for linear elastodynamics of periodically laminated media

Abstract The asymptotic method of multiple scales is used to construct a continuum theory with microstructure for the linear elastodynamics of a periodically laminated medium. The resulting theory is in the form of a homogeneous binary mixture theory of micromorphic materials with a common director oriented normal to the interfaces. The model contains nine conservation equations—six for the linear momenta of both constituents and three for the director momentum. The asymptotically derived constitutive equations contain mixture properties which, in contrast to phenomenological theories, are determined solely from the properties of the individual constituents and their volume fractions. The mixture conservation and constitutive equations are complemented by an appropriate set of boundary conditions determined by a variational procedure. The efficacy of the model is assessed by comparison of predicted and exact phase velocity spectra for waves propagating at oblique incidence to the layers. The excellent agreement observed indicates that the model is useful for studying the dynamic behavior of laminated composites. Further, the method of multiple scales appears to provide an effective approach to the accurate determination of the large scale behavior of a material which exhibits small scale periodic heterogeneity.

A high-order mixture model for periodic particulate composites

Abstract A deterministic mixture theory is presented for periodic paniculate composites. The model is constructed by introducing convenient microdisplacement and microstress variables, and by using a regular asymptotic technique with multiple scales. Governing equations and appropriate boundary conditions are then deduced from Reissner’s mixed variational principle ( J. Math. Phys. 29 , 90–95 (1950)). In order to test the accuracy of the present model, harmonic wave propagation is examined and compared with available experimental data for glass/epoxy and steel/PMMA composites reported by Kinra and Ker ( Int. J. Solids Structures 19 , 393–410 (1983)). Also, the effective elastic moduli are computed, and the results compared with other analytical methods.

Anisotropic Beam Theories With Shear Deformation

We investigate the effect of constitutive coupling of stretching, bending, and transverse shearing deformation on the deflection of an anisotropic cantilever beam with narrow rectangular cross-section. To this end, we have developed a hierarchy of beam models by applying a variational principle for displacements and transverse stresses to the associated plane stress problem.