Static analysis of thin-walled space frame structures with arbitrary closed cross-sections using transfer matrix method

Zhong, Haolong; Liu, Zijian; Qin, Huan; Li, Yu

doi:10.1016/j.tws.2017.11.018

Cited by 13 publications

(3 citation statements)

References 29 publications

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“…Equation ( 4) may be solved by using a technique developed for the solution of two-point boundary value problems (BVP), or it may be handled by a technique like transfer matrix [1,49,[62][63][64][65][66][67][68][69] and complementary functions methods [24,61,[70][71][72][73][74][75] or any of the others developed for the solution of initial value problems (IVP).…”

Section: Mathematical Formulation and Solution Of The Problemmentioning

confidence: 99%

Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods

Yıldırım

2022

International Journal of Engineering and Applied Sciences

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In the present paper, the transfer matrix method (TMM) is to be employed for the first time in the open literature for the elastic analysis of variable-thickness disks made of functionally graded (FG) two orthotropic materials. Those materials are assumed to be continuously radially functionally graded (FG) based on the Voigt rule of mixture with two models. An exponential disk profile with two parameters is considered. Effects of the different boundary conditions (free-free, fixed-free, and fixed-fixed) and inhomogeneity indexes on the elastic response of the disk rotating at a constant angular speed are also examined. Additionally, direct numerical solutions of the problem with the complementary functions method (CFM) are presented in tabular forms together with the transfer matrix method solutions in which CFM was used as an assistant tool. It was observed that both location and amplitude of the maximum equivalent stress are affected by the grading models chosen. Such differences become more obvious for small values of the inhomogeneity indexes. The maximum relative error may reach 18% for the two material grading models in fixed-free disks. Consequently, Model-I may be recommended for just the inhomogeneity indexes equal to or greater than 0.5.

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Section: Mathematical Formulation and Solution Of The Problemmentioning

confidence: 99%

Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods

Yıldırım

2022

International Journal of Engineering and Applied Sciences

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“…Hance, closed analytical solutions for the bendingtorsional-warping coupled frequency response of thin-walled beams with multiple DOF spring-damper-mass subsystems is significant for the parameter design of multiple DOF absorbance and elastic suspension in vibration reduction application. Furthermore, despite the valuable insights provided by transform methods [48,49], no analytical expressions are available for the bending-torsional-warping coupled frequency response of thin-walled beams with multiple DOF spring-damper-mass subsystems; this requires a specific complex transformation approach with dynamic condensation.…”

Section: Introductionmentioning

confidence: 99%

On the Forced Vibration of Bending-Torsional-Warping Coupled Thin-Walled Beams Carrying Arbitrary Number of 3-DoF Spring-Damper-Mass Subsystems

Chen

Liu

2022

Mathematics

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This paper presents an analytical transfer matrix modeling framework for the forced vibration of a bending-torsional-warping coupling Euler-Bernoulli thin-walled beam carrying an arbitrary number of three degree-of-freedom (DOF) spring-damper-mass (SDM) subsystems. The thin-walled beam is divided into a series of distinct sub-beams whose ends are connected to the SDM subsystems. The transfer matrix for each sub-beam is developed based on the exact shape functions of the bending-torsional-warping coupling Euler-Bernoulli theory. Each SDM system is modelled by a set of effective springs based on the dynamic condensation method. The governing matrix equation is formulated based on the compatibility conditions of the placement and the force at the common interfaces of two adjacent sub-beams. Then, a closed-form expression for the frequency response function of the thin-walled beam system is proposed. The results computed by the proposed method achieve good agreement with those obtained by the conventional finite-element method, which shows the accuracy and reliability of the proposed method. The effects of the system parameters on the vibration transmission and vibration isolation properties of the thin-walled beam system are studied. The presented method can simultaneously consider arbitrary number of SDM subsystems and boundary conditions. Furthermore, none of the associated matrices are larger than 12 × 12, which provides a significant computational advantage.

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“…Miranda and Reyes (2002) developed approximate methods to estimate the maximum lateral displacement and interstory drift ratio of the buildings with uniform/nonuniform lateral stiffness along the height. To analyze the shear wall-frame with vertically variable cross-section, the transfer matrix method is extensively applied (Bozdogan, 2009;Zhong et al, 2018). It can get the exact results, but extensive hand-calculations are inevitable.…”

Section: Introductionmentioning

confidence: 99%

Efficient analysis of shear wall-frame structural systems

Xia

Shu

Stanciulescu

2019

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Purpose This paper aims to propose an efficient method to conduct the preliminary analyses of medium or high-rise wall-frame structural systems with vertically varying properties. To this end, a finite element is formulated to take the shear deformation of the shear wall and the constrained moment of the link beam. Design/methodology/approach The differential equation of the structure is derived from the total potential energy. Its homogenous solutions are functions of initial parameters (deflections and inner forces). To solve the structure with vertically non-uniform properties, the authors first use the classical Timoshenko beam element and then heuristically propose a finite element that uses the initial parameter solutions as shape functions and is easier to implement. A post-processing method to compute the shear force in the frame and shear wall is developed. Modal analysis using the consistent mass matrix is also incorporated. Numerical examples demonstrate the accuracy and mesh independency of the proposed element. Findings The shear deformation of the shear wall and the constrained moment of the link beam significantly influence the static response of the structure. Taking into account the shear deformation can eliminate the misleading result of zero-base shear force of the frame and give much better predictions of the system natural frequencies. Originality/value The proposed method achieves higher accuracy than the classical approach most often used. The finite element formulation derived from transformations of the initial parameter solutions is simple and has superior numerical performance. The post-processing method allows for a fast determination of the shear force distributions in the shear wall and frame.

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Static analysis of thin-walled space frame structures with arbitrary closed cross-sections using transfer matrix method

Cited by 13 publications

References 29 publications

Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods

Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods

On the Forced Vibration of Bending-Torsional-Warping Coupled Thin-Walled Beams Carrying Arbitrary Number of 3-DoF Spring-Damper-Mass Subsystems

Efficient analysis of shear wall-frame structural systems

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