3D Frame Structure Research Articles

Elasto-Plastic Analysis of Frame Structures under Large Displacement-Rotation Deformations

A finite element program for elasto-plastic analysis of 3D beams and frame structures under large displacement/rotations is developed. The element is Timoshenko beam element based on mechanics of continuum. Constitutive equations for large displacements/rotations in elastic stage are expressed in an explicit way which is suitable for programming. The modification of constitutive equation is presented for the analysis of elasto-plastic problems. A fiber model is adopted for the calculation of stiffness matrix and internal forces. For solution of nonlinear finite element equations, general displacement control method and semi-modified stiffness matrix method is adopted. The results of numerical experimentation show that the program work well for 3D beams and frame structures under elasto-plastic large displacement/rotations.

Progressive Collapse Mechanisms of Brittle and Ductile Framed Structures

In this paper, we study the progressive collapse of 3D framed structures made of reinforced concrete after the sudden loss of a column. The structures are represented by elasto-plastic Euler Bernoulli beams with elongation-rotation failure threshold. We performed simulations using the Discrete Element Method considering inelastic collisions between the structural elements. The results show what collapse initiation and impact-driven propagation mechanisms are activated in structures with different geometric and mechanical features. Namely, we investigate the influence of the cross sectional size and reinforcement $\alpha$ and of the plastic capacity $\beta$ of the structural elements. We also study the final collapse extent and the fragment size distribution and their relation to $\alpha$, $\beta$ and to the observed collapse mechanisms. Finally, we compare the damage response of structures with symmetric and asymmetric reinforcement in the beams.

Simple Iterative Use of Lyapunov's Solution for the Linear Optimal Seismic Design of Passive Devices in Framed Buildings

This article presents a Lyapunov-based analysis/redesign approach for the optimal seismic design of added viscous dampers in 3D framed structures. The optimal solution minimizes the total added damping while the mean squared drifts at the peripheral frames are constrained to allowable values under a white noise excitation. The proposed approach uses Lyapunov equation for analysis and an optimality criterion that dictates “fully stressedness” for redesign. Hence, the design process is actually comprised of an iterative solution of a set of algebraic equations. Three examples are solved so as to highlight the advantages of the proposed approach — a 3-story shear frame, an 8-story, 3-bay by 3-bay setback frame, and a 10-story industrial frame.

Damage Analysis of 3D Frame Structure under Impulsive Load

In this article, we utilized the lumped damage mechanics method to implement the damage analysis to the 3D frame structure under impulsive load. First, take the damage parameters as the interior variable of the system, and based on the finite unit, combine continuum mechanics, fracture mechanics and plastic hinge to analyze the mechanical behaviors of the structure, and finally implement numerical simulation analysis to the frame structure with two layers, and compare the result with the computation result of ABAQUS to validate the feasibility.

Free Vibration Analysis of Frames Using the Transfer Dynamic Stiffness Matrix Method

A method for free vibration of 3D space frame structures employing transfer dynamic stiffness matrix (TDSM) method based on Euler–Bernoulli beam theory is developed in this paper. The exact TDSM of each member is assembled to obtain the system matrix that is frequency dependent. All free vibration eigensolutions including coincident roots for the characteristic equation can be obtained to any desired accuracy using the algorithm developed by Wittrick and Williams (1971, “A General Algorithm for Computing Natural Frequencies of Elastic Structures,” Q. J. Mech. Appl. Math., 24, pp. 263–284). Exact eigenfunction of structures can then be computed using the dynamic shape function and the corresponding eigenvector. The results showed good agreement with those computed by finite element method.

Crash behavior of a 3D S-shape space frame structure

Abstract In order to ensure enough passenger space and reduce the damage of occupants during a car front collision, it is necessary to understand the crushing behavior and to improve the energy absorption capability of space frame structures. In this study, the crushing behavior of a 3D S-shape extruded aluminum square frame with 45° curvature angle (α) and 45° rotation angle (β) is studied under an axial loading. Different cross-section reinforcements (parallel and diagonal internal lateral support profiles) and aluminum foam-filled reinforcement are discussed. The effectiveness of reinforcement is assessed using the specific energy absorption and the peak force. Based on the numerical analyses, the left diagonal reinforced structure shows the highest specific energy absorption (SEA = 3.813 J/g). This is 277% of the SEA of the empty column structure (SEA = 1.375 J/g). In addition, the aluminum foam-filled reinforcement increases the energy absorbed by the 3D space frame structure by an additional 78%. The results show that aluminum foam is an efficient alternative energy absorber. However, it does not increase the SEA of the structure due to the increased mass and increases the peak force significantly.

Modal Strain Energy Decomposition Method for Damage Localization in 3D Frame Structures

This article presents a newly developed modal strain energy decomposition method for damage localization that is capable of identifying damage to individual members of three-dimensional (3D) frame structures. This method is based on decomposing the modal strain energy of each structural member (or element) into two parts, one associated with the element’s axial coordinates and the other with its transverse coordinates. In turn, two damage indicators are calculated for each member to perform the damage localization analysis. Implementing this method requires only a small number of mode shapes identified from both the damaged and baseline structures. Numerical studies are conducted of a 3D five-story frame structure and also a complicated offshore template platform, based on synthetic data generated from finite-element models. In addition to providing theoretical insights to illustrate the advantages of using this newly developed method, this article also demonstrates numerically that the new method is capa...

Structural optimization: A tool for evaluating seismic design procedures

The objective of this paper is to evaluate seismic design procedures for three-dimensional (3D) frame structures using structural optimization methodologies. The evaluation is based on European seismic design code, where procedures based on both linear and nonlinear time-history analysis are adopted. In order to simulate seismic actions realistically, suites of both natural and artificial ground motion records are used. Furthermore, it is shown that structural optimization is a very efficient design tool that can be applied on realistic buildings. For the solution of the optimization problem, a highly efficient evolutionary algorithm is adopted. The results obtained demonstrate the advantages of using more elaborate seismic design procedures, based on a detailed simulation of the structural behaviour and the applied seismic loading, as opposed to the commonly used simplified design approaches. Designs with less material cost combined with better seismic performance are obtained when nonlinear time-history analysis is performed.

A Topology Optimization Problem in Control of Structures Using Modal Disparity

Modal disparity and a topology optimization problem seeking to maximize this disparity are introduced, with the goal of developing a new methodology for control of vibration in flexible structures. Modal disparity is generated in a structure by the application of external forces that vary the stiffness of the structure. When the forces are switched on and off and, as a result, the structure is switched between two stiffness states, modal disparity results in vibration energy being transferred from a set of not-controlled modes to a set of controlled modes. This allows the vibration of the structure to be completely attenuated by removing energy only from a small set of controlled modes. A topology optimization problem determines the best locations for application of the external forces. Simulation results are presented to demonstrate control of vibration exploiting modal disparity in two three-dimensional (3D) frame structures.

An alternative formulation of the FE method for arbitrary discrete/continuous models

The paper describes new object-oriented formulation of a general FE algorithm that encompasses traditional FE elements, super elements, experimental data, codes of practice and rigid-body mechanics in a single calculation environment. The new formulation is implemented in software for dynamic crash simulation of an arbitrary 3D frame structure discretized into superbeam elements and subjected to large dynamic crash loadings. The paper presents basics of the general algorithm and element formulation. The theoretical part is followed by two examples of application of the new code to real-word structures.

Seismic fragility analysis of 3D structures

A statistical approach for time-variant system reliability problems is developed and investigated. The basic proposal is to use a response surface, characterised by a statistical model of the mixed type, to represent the capacity in an analytical limit-state function. The fragility function of the system is then calculated by FORM analysis, with the constructed empirical limit-state function as input. The methodology is applied in the assessment of a 3D RC frame structure. The application allows a number of detailed implementation issues to be clarified, and confirms the robustness and versatility of the method.

Classic Buckling of Three-Dimensional Multicolumn Systems under Gravity Loads

The elastic stability of three-dimensional ~3D! multicolumn systems under gravity loads is analyzed in a condensed manner using the classical Timoshenko stability functions. The characteristic equations corresponding to multicolumn systems with sidesway uninhibited, partially inhibited, and totally inhibited are derived. Using the transcendental equations of the proposed method, the effective length K factor for each column and the total critical axial load of an entire story can be determined directly. The proposed method is applicable to 3D framed structures with rigid, semirigid, and simple connections. It is shown that the elastic stability of framed structures depends on: ~1! the axial load pattern on the columns; ~2! the variation in size and height among the columns; ~3! the plan layout of the columns; ~4! the overall floor-torsional sway caused by any asymmetries in the loading pattern, column layout, and column sizes and heights ~all of which reduce the flexural-buckling capacity of multicolumn systems !; ~5! the end restraints of the columns; and ~6! the bracings along the two horizontal and rotational directions of the floor plane. The proposed method solves the classical bifurcation stability of 3D frames directly without complex matrix solutions, however, it is limited to frames made up of columns of doubly symmetrical cross section with their principal axes parallel to the global axes. Examples are presented that show the effectiveness of the proposed method and the results compared with those obtained by complex matrix methods.

Conceptual issues in geometrically nonlinear analysis of 3D framed structures

This paper aims to clarify some of the conceptual issues which are related to the geometrically nonlinear analysis of 3D framed structures, and which have been a source of previous confusion. In particular, the paper discusses the symmetry of the tangent stiffness matrix and the nature of the element end moments. It is shown that a symmetric tangent stiffness matrix can always be achieved for a conservative system if the nodal equilibrium equations, including the equations which describe moment equilibrium, are identical to those derived from a variational energy approach. With regard to the element end moments, it is suggested that any definition can be adopted in formulating the geometrically nonlinear element response. Furthermore, it is proposed that any definition for nodal rotations expressing a unique vector transformation may be adopted without compromising modelling accuracy. The argument of this paper is validated with reference to three variants of a large displacement analysis method for 3D frames, where several illustrative examples are utilised.

Nonlinear Analysis of Mixed Steel-Concrete Frames. I: Element Formulation

A beam-column element for simulating the inelastic behavior of 3D mixed frame structures comprised of steel, reinforced concrete, and/or composite members is presented. The formulation makes use of the flexibility method for deriving the element stiffness equations. A stress-resultant bounding surface plasticity model provides the sectional properties, which are then integrated along the length to generate the stiffness matrices. For steel members, the plasticity model is based on two nested surfaces, whereas for composite and reinforced concrete members the inner loading surface is degenerated to a point. Stiffness degradation of reinforced concrete and composite members is incorporated as a function of dissipated strain energy. Implementation and verification of the models for static and dynamic time-history analyses of mixed steel-concrete space frames are presented in a companion paper.

Sensitivity analysis and optimal design of 3D frame structures for stress and frequency constraints

The present paper deals with the problem of determining the optimal joint positions and cross-sectional parameters of linearly elastic space frames with imposed stress and free frequency constraints. The frame is assumed to be acted on by different load systems, including temperature and self-weight loads. The stress state analysis includes tension, bending, shear, and torsion of beam elements. By a sequence of quadratic programming problems, the optimal design is attained. The sensitivity analysis of distinct as well as multiple frequencies is performed through analytic differentiation with respect to design parameters. Illustrative examples of optimal design of simple and medium complexity frames are presented, and the particular case of bimodal optimal solution is considered in detail.

Effect of Soil Consolidation on Space Frame-Raft-Soil Interaction

Nonlinear consolidation analysis using a finite-element (FE) formulation based on Biot's consolidation theory has been used to study the time-dependent behavior of three-dimensional (3D) frame structures resting on an elastic or elastic perfectly plastic soil satisfying the Drucker-Prager yield criterion. The effect of soil consolidation on the behavior of a 3D frame-raft-soil mass system is considered. The initial stress method with a modified Newton-Raphson iterative scheme has been used for this study. A coupled finite-infinite element modelization is used for the physical representation of the system. Time history of axial forces and bending moments of the mat foundation and the structural elements (beams and columns) are compared with those of time-independent analysis. The results show that the consolidation of soil increases the internal forces in some elements, so that checking the final forces in the frame by time-independent conventional frame analysis may not be sufficient.

3D image reconstruction of bladder by nonlinear interpolation

In this paper, we propose a new 3D reconstruction method to produce the 3D shading image of the bladder from a series of 2D cross-sectional CT images. To achieve this goal, the deformable model method, based on the concept of energy driven and model matching, are employed to locate the contour of the bladder. After a series of 2D contours image is obtained, a 3D wire frame structure can be constructed by stacking these 2D contours in sequence. Next, a nonlinear interpolation scheme of the Hermite surface is used to interpolate the spatial data from the contours To create the depth effect and remove the hidden surface of the 3D image of the bladder, the diffuse reflection model, the Gourand shading technique, and the back-to-front display scheme are utilized, respectively. Experimental results that verify the effectiveness of this approach are given.

Effect of raft flexibility and soil media on the dynamic response of a framed structure

In this paper, a numerical model is outlined for a three-dimensional (3D) dynamic soil-structure system using 3D frame elements for modelling the superstructure, the combination of thick plate elements and plane stress elements for modelling the raft foundation and the coupled method of 3D finite elements and infinite elements to model the infinite soil medium. After verifying the accuracy of the present method, a general study on the effects of raft flexibility and soil media on the dynamic response of a 3D frame structure including dynamic interaction effects is also performed. The associated numerical results from this study have demonstrated that (1) the present model is very suitable to solve the dynamic frame-foundation-soil interaction problems; (2) the combination of thick plate element and plane stress element should be used to model the raft in the analysis when the system is subjected to the excitation of horizontal earthquakes; (3) the flexibility of a raft must be included in the dynamic analysis of a 3D frame-foundation-soil system so that a realistic solution can be obtained; (4) the layer characteristics of soil media underneath the raft have significant effects on the dynamic response of a 3D frame structure and the softer soil layer will result in greater response of the frame.

An easily implemented static condensation method for structural sensitivity analysis

AbstractIn many situations, the sensitivity of the response of a structure to parameters affecting only a small part of the structure is desired. In such cases, it is efficient to use substructuring or static condensation approaches. However, static condensation is not available in all finite‐element codes, and its implementation requires access to and familiarity with the source code of the program. The present paper suggests an alternative version of static condensation for sensitivity calculations which is easy to implement without access to the source code of the finite‐element program. The proposed approach (black‐box method) is demonstrated by applying it in system identification of joint parameters of 3D frame structures using a direct method for evaluating the sensitivity derivatives of the structural response with respect to the joint parameters.