Daigoro Isobe

Analysis of structurally discontinuous reinforced concrete building frames using the ASI technique

Abstract The Adaptively Shifted Integration (ASI) technique, which produces the highest computational efficiency in the finite element analyses of framed structures including static and dynamic collapse problems, is applied to structurally discontinuous problems of reinforced concrete building frames. A new numerical scheme based on the updated Lagrangian formulation (ULF) adaptation of the ASI technique is developed, by modeling the fracture of a section by a plastic hinge located at the exact position with a simultaneous release of resultant forces in the element. By using the algorithms described in this paper, the analyses became possible even by the conventional displacement-based finite element codes, and sufficiently reliable solutions for practical use have been obtained in the explosive demolition and seismic damage analyses of a five storied, five span RC building frame. The present technique can be easily implemented with minimum effort into the existing finite element codes utilizing the linear Timoshenko beam element.

Finite element analysis of quasi-static and dynamic collapse behaviors of framed structures by the adaptively shifted integration technique

The adaptively shifted integration technique (abbreviated to the ASI technique) is applied to the dynamic collapse problems of framed structures including the quasi-static collapse under repeated loading. The unloading of materials plays an important role in these behaviors. In the present analysis using cubic beam elements, the reshifting of the integration points to the Gaussian points in the unloaded elements is conducted in order to attain higher accuracy for the material-unloading behavior. The solutions given by conventional method, the ASI technique with and without reshifting are compared to show the validity of the newly proposed computational algorithm.

A unified solution scheme for inverse dynamics

In this paper, a completely new solution scheme for inverse dynamics, which can be commonly applied in different types of link systems such as open- or closed-loop mechanisms, or ones constituting rigid or flexible link members, is presented. The scheme is developed using the finite element method (FEM), which evaluates the entire system as a continuum with the equation of motion in Cartesian coordinates and in dimension of force. The inverse dynamics is calculated by using a matrix-form relation to the nodal forces obtained by the FEM. The matrix-form equations are divided individually into terms of force, transformation between coordinates and length, which makes the scheme potentially better in terms of applicability and expansibility. The scheme cannot only deal with open- and closed-loop link systems independently, but it can also deal seamlessly with those that gradually change their forms and dynamics. There is also no need to revise the basic numerical algorithm of the scheme, regardless of the stiffness of the constituting link member, i. e. rigid or flexible. The main objective of this paper is to present the extensive ability of the scheme as a unified scheme, by carrying out calculations on several types of rigid and flexible manipulators, along with an application to feed-forward control of a link mechanism which continuously changes its form from an open- to a closed-loop.

A Parallel Control System for Continuous Architecture Using Finite Element Method

In this paper, a parallel control system for continuous architecture formed by bimorph piezoelectric actuators has been developed and verified. Finite Element Method (FEM) is adopted as the control scheme for it is capable of expressing the behavior of the whole system by evaluating the stiffness equations. Conventional control system requires a slight change in its state equations, depending on the shape of a system or the quantity of the linked members. Although FEM is mainly a computational tool for analyzing structures, fluids, etc., the capability of expressing the whole continuous system can be applied to parallel control schemes, and may be practical if the computational time is reduced to real-time use. An inverse theory, which is simplified by using the linearity of the electric potential distribution in a bimorph piezoelectric actuator, is applied for calculating control voltage of the actuators. The algorithm using this theory consumes less computational memory, and runs faster than the numerical schemes using generalized inverse matrices. This paper seeks the reduction of dofs and thus the computational time, by implementing noncompatible four-node element to the FEM control program. The finite element allows in-plane bending mode by considering noncompatible mode in shape functions, and can obtain practical solutions by minimum number of elements. By examining the experiments on static displacement control of connected piezoelectric actuators, the validity of the FEM parallel control system has been confirmed.

A unified numerical scheme for calculating inverse dynamics of open/closed link mechanisms

In this study, a scheme using the Finite Element Method (FEM) for calculating inverse dynamics is proposed and applied to open- and closed-loop link mechanisms. In this scheme, the entire system is subdivided into discrete elements and evaluated as a continuum. A single-link structure of a pin joint and a rigid bar is expressed by using the Shifted Integration (SI) technique. The proposed scheme calculates nodal forces by evaluating equations of motion in a matrix form, and thus information from the entire system can be handled in parallel. The obtained nodal forces are then used to calculate the joint torque in the system. Simple numerical tests on open- and closed-loop link mechanisms are carried out, and it is verified that the scheme can be used as a unified numerical scheme independent of the system configuration.

Feedforward control of flexible link systems using parallel solution scheme

In this paper, a parallel solution scheme of inverse dynamics is revised and applied to flexible link systems where elastic deformation and vibration normally occur in constituting links. The scheme is considered to be valid for link systems with elastic members, as the calculation process of the scheme is based upon a finite element approach. It evaluates the analysed model in absolute Cartesian coordinates with the equation of motion expressed in dimension of force. The calculated nodal forces are converted into joint torques using a matrix form equation divided into terms of force, transformation between coordinates, and length. Therefore, information from the entire system can be handled in parallel, which makes the calculation seamless in application to any type of link system regardless of its boundary conditions or stiffness values. In this paper, the scheme is revised and the calculation time is shortened by applying Bernoulli-Euler beam elements, and it is then combined with a kinematics solution scheme that calculates target trajectories for flexible models. The calculation flow of inverse dynamics is shown for a five-link system, and some feedforward control experiments are carried out on a two-link system with different stiffness links. The accuracies of trajectories and torque values are verified by applying the system to a sensorless, model-based vibration control. The trajectories and torque values are confirmed to be highly accurate compared with the actual data for feedforward control, and the validity of the approach is verified.

Numerical Simulations on the Collapse Behaviors of High-Rise Towers

In this paper, several numerical simulations of framed structures were performed to identify the specific structural cause of the high-speed total collapse of the World Trade Center (WTC) towers, which occurred during the 9/11 terrorist attacks. A full-scale aircraft impact simulation of the WTC tower 2 was conducted to examine the dynamic unloading phenomena that occurred in the core columns during impact, which may have caused the destruction of the splices between column sections. Fire-induced progressive collapse analyses of a high-rise tower with an outrigger truss system were carried out to qualitatively demonstrate the effects of fire patterns and structural parameters on the behavior of this towers collapse. In general, the tower remained standing for a longer period of time due to the catenary action of the outrigger truss system only if the load paths in the tower were protected and if the member connections were strong enough. However, in these analyses, the collapse speed never reached a value as high as that of the free fall observed in the WTC collapse, which occurred while the splices between column sections still retained their tensile strength. From these results, it is evident that the high-speed collapse of the WTC towers might have been caused by an inherent weakness in their member connections in addition to the destruction directly caused by the aircraft impact.

Simulating Collapse Behaviors of Buildings and Motion Behaviors of Indoor Components During Earthquakes

A finite element code, which can handle large-scale collapse and motion behaviors of structural and non-structural components of buildings, was developed. The code was developed with a use of an adaptively shifted integration (ASI)-Gauss technique. It provides higher computational efficiency than the conventional code in those problems with strong nonlinearities including phenomena such as member fracture and elemental contact. Several numerical results obtained by using the numerical code are shown in this chapter: first, a seismic pounding analysis of the Nuevo Leon buildings, in which two out of the three buildings collapsed completely in the 1985 Mexican earthquake, then, a continuous analysis of a steel frame building, subjected to a seismic excitation followed by application of tsunami force, and finally collided with a debris. A motion behavior analysis of a gymnasium is followed as a numerical example, showing the behaviors of indoor components such as ceilings, which dropped occasionally due to detachment of clips and screws. Furthermore, numerical results on motion behavior analysis of furniture were validated with some experimental results.

Dynamics computation of link mechanisms employing COG Jacobian

We show the dynamics computation employing Jacobian that relates the center of gravity (COG) to joints of link mechanisms, in this paper. COG Jacobian is used for the behavior planning and the control of humanoids. And, it usually expresses the relationship between the joints and COG of a robotpsilas whole body. However, in this scheme, itpsilas calculated regarding each link and not the robotpsilas whole-body. Moreover, we can obtain the torques by relationship between COG Jacobian and the applied forces to COG by using principle of virtual work. The loaded forces to COG can be obtained by employing Newtonpsilas and Eulerpsilas equations of motion. By the scheme, we can calculate the inverse dynamics regardless of open- and closed-link mechanisms. In addition, the forward dynamics can be calculated by employing COG Jacobian.

Motion planning of manipulators regarding structural safety as a prior condition

In this paper, a motion-planning scheme that enables manipulators to avoid structural damage is described. Using this scheme, manipulators are encouraged to protect themselves from structural damage by searching for a safer attitude when their structural risk becomes high during their given tasks. The structural risk is determined by using two parameters, i.e., the resultant forces and total strain energy stored in the architecture, which are calculated by the finite element method. Three schemes of motion planning that use the structural parameters are compared by carrying out numerical tests with structurally severe tasks. Furthermore, the proposed strategy is implemented in the interface of a robotic arm to verify its validity. The experimental results revealed the practicability of the scheme in avoiding structural damage to the constituent members.