Koji Uetani

Non-monotonic optimal damper placement via steepest direction search

An efficient and systematic procedure is proposed for finding the optimal damper positioning to minimize the dynamic compliance of a 3-D shear building model. The dynamic compliance is expressed in terms of the transfer function amplitudes of the local interstorey drifts evaluated at the undamped fundamental natural frequency. The dynamic compliance is minimized subject to a constraint on the sum of the damping coefficients of added dampers. Optimality criteria are derived and the optimal damper positioning is determined via an original steepest direction search algorithm. This algorithm enables one to find an optimal damper positioning sequentially for gradually increasing damper capacity levels. A non-monotonic design path with respect to the total damper capacity level often appears in the application of this algorithm. A new augmented algorithm via parameter switching is devised to find this non-monotonic design path. Copyright

Application of an optimum design method to practical building frames with viscous dampers and hysteretic dampers

An innovative optimum design system for structures with passive-type dampers is proposed. The design system depends on the type of dampers. A realistic application example is presented first of the optimum structural design method to practical building frames with hysteretic dampers. A computer program based on the gradient projection algorithm is used for initial design of a 100 m-high building frame located at Osaka, Japan. The effect of hysteretic dampers is incorporated in the calculation of design horizontal loads. The present method has the flexibility that manual modification by structural designers can be added to the initial design in order to satisfy multiple design conditions specified in the Japanese building structural design codes. Subsequently another practical method is presented for optimum structural design of building frames with viscous dampers. This method is a two-step design procedure. The first step consists of the stiffness design of a reduced shear-building model with viscous dampers. The second step is the optimum design for building frames subjected to static design loads. The design horizontal static loads are determined in the first step. Several design examples are presented to demonstrate the usefulness of the proposed design method.

The secondary buckling and post-secondary-buckling behaviours of rectangular plates

Abstract Secondary buckling and post-secondary-buckling behaviours are theoretically studied for simply-supported rectangular plates, whose primary buckling modes of deflection contain more than half-waves in the load acting direction. Modal coupling effects more complex than one two-term-coupling effects are incorporated into the secondary buckling and post-secondary-buckling analyses. Then, unstable or stable symmetric secondary branching points are found on the post-primary-buckling paths and “snap through” motions involving an abrupt change in wave-form are shown to be possible. Wave-form variations along post-secondary-buckling paths are also disclosed by means of a numerical analysis of equilibrium paths.

Optimal damper placement for building structures including surface ground amplification

A systematic method for optimal added damper placement in building structures is developed, taking into account the response amplification due to the surface ground. Non-linear amplification of the surface ground is described by an equivalent linear model. Hysteretic damping of the surface ground and radiational damping into the semi-infinite visco-elastic ground are included in the model. An original steepest direction search algorithm is applied to the interaction model. Closed-form expressions of the inverse of the coefficient matrix (tri-diagonal matrix) enable one to compute the transfer function and its derivative with respect to design variables very efficiently. It is shown that the ratio of the fundamental natural period of the structure to that of the surface ground is a key parameter for characterizing the optimal damper placement. Several examples for different soil conditions are presented to demonstrate the effectiveness and validity of the present method.

Symmetry limit theory for cantilever beam-columns subjected to cyclic reversed bending

Abstract The behavior of a linear strain-hardening cantilever beam-column subjected to completely reversed plastic bending of a new idealized program under constant axial compression consists of three stages: a sequence of symmetric steady states, a subsequent sequence of asymmetric steady states and a divergent behavior involving unbounded growth of an anti-symmetric deflection mode. A new concept “symmetry limit” is introduced here as the smallest critical value of the tip-deflection amplitude at which transition from a symmetric steady state to an asymmetric steady state can occur in the response of a beam-column. A new theory is presented for predicting the symmetry limits. Although this transition phenomenon is phenomenologically and conceptually different from the branching phenomenon on an equilibrium path, it is shown that a symmetry limit may theoretically be regarded as a branching point on a “steady-state path” defined anew. The symmetry limit theory and the fundamental hypotheses are verified through numerical analysis of hysteretic responses of discretized beam-column models.

Optimization of imperfection-sensitive symmetric systems for specified maximum load factor

A method is presented for optimum design of a symmetric structure which reaches an unstable bifurcation point as the load factor is increased. Reduction of the maximum load level due to the antisymmetric imperfection is considered, and a straightforward algorithm is proposed for calculating the magnitude of reduction of the load factor corresponding to the most critical mode of antisymmetric imperfection. The sensitivity coefficients of the bifurcation load factor are calculated by using the interpolation method developed by the authors, and an approximate formulation is presented for sensitivity analysis of the maximum load factor. It is shown in the examples that the errors in the sensitivity coefficients do not lead to any significant difference in the optimum design.

Criteria for suppression of deformation concentration of building frames under severe earthquakes

It has been revealed by symmetry limit theory that an unknown type of collapse behavior, characterized by cyclic growth of a bow-shaped mode overall deflection, could occur in a multistory multibay weak-beam planar frame subjected to a static cyclic program of top horizontal displacement. Dynamic response analysis of the multistory frame, performed later, has shown that the bow-shaped mode deflection is possible to appear in a restricted lower part of the frame and, thereby, deformation concentration occurs in that part in the process of dynamic collapse. In this paper, criteria for suppression of growth of the bow-shaped mode deflection and the deformation concentration will be proposed. Even if a frame is designed so that the criteria are satisfied, a gradual one-way drift of the sway-mode vibration center may still be observed under a cyclic ground motion. Criteria for suppression of the sway drift will also be proposed to meet higher-level safety requirements.

Fast practical evaluation of soil -structure interaction of embedded structures

Abstract A simple and fast evaluation method of soil–structure interaction (SSI) effects of embedded structures is presented via a cone model. The impedances and the effective input motions at the bottom of an embedded foundation are evaluated by means of the cone model. Those quantities are transformed exactly to the corresponding values at the top of the foundation. The evaluated quantities are combined with the super-structure at the top of the foundation. The transfer function amplitude of the interstory drift of a single-degree-of-freedom super-structure is computed for various cases, i.e. no SSI, SSI without embedment, SSI with shallow embedment, SSI with deep embedment. Soil properties are also varied to investigate in more detail the SSI effects of embedded structures. It is found that, while the transfer function amplitude is reduced by the increase of embedment in general, the characteristics of the transfer function amplitude for a very small ground shear wave velocity and large embedment are irregular and complicated.

SENSITIVITY ANALYSIS OF BIFURCATION LOAD OF FINITE-DIMENSIONAL SYMMETRIC SYSTEMS

Three methods are presented for sensitivity analysis of bifurcation load factor of finite-dimensional conservative symmetric systems subjected to a set of symmetric proportional loads. In the first method, a conventional method with diagonalization is utilized to derive an explicit formula of sensitivity coefficients corresponding to a minor imperfection. Next, a new concept is introduced to find the sensitivity coefficients of the load factor, displacements and the eigenmodes under fixed lowest eigenvalue of the tangent stiffness matrix. Based on this concept, a method is presented for finding approximate sensitivity coefficients of the buckling load factor. Finally, a direct method is presented to find the accurate sensitivity coefficients of the bifurcation load factor, displacements at buckling and the buckling mode of a symmetric system. Note that different formula should be used for sensitivity analysis of a limit point load factor. In the examples, the proposed three methods are compared in view of accuracy of the results and simplicity in coding.

Inverse component-mode synthesis method for damped large structural systems

Abstract A new formulation for an incremental inverse problem is proposed to enhance computational efficiency of redesign of damped large structural systems. A large structural system is regarded as an assemblage of substructures. In the present formulation, mechanical properties of some substructures are given, and those of the other substructures are taken as the design variables. This problem is a hybrid inverse problem. Those design variables are determined so that the fundamental natural frequency and the transfer function amplitude ratios would attain the target values. It is shown that the inverse use of the conventional component-mode synthesis (CMS) technique within the scope of the hybrid inverse problem enables one to develop an efficient computational procedure for updating the design variables in the design problem. The proposed method can deal with a damped structural system with a general damping system (proportional or non-proportional, viscous and/or hysteretic, Voigt-type or Maxwell-type), in a unified manner. Different from the conventional CMS method utilized for redesign, component modes of the substructure are fixed during the redesign process. The validity and order of approximation of the proposed method is demonstrated through an example model.