Purpose
This paper aims to present an adaptive approach of the generalized finite element method (GFEM) for transient dynamic analysis of bars and trusses. The adaptive GFEM, previously proposed for free vibration analysis, is used with the modal superposition method to obtain precise time-history responses.
Design/methodology/approach
The adaptive GFEM is applied to the transient analysis of bars and trusses. To increase the precision of the results and computational efficiency, the modal matrix is responsible for the decoupling of the dynamic equilibrium equations in the modal superposition method, which is used with only the presence of the problem’s most preponderant modes of vibration. These modes of vibration are identified by a proposed coefficient capable of indicating the influence of each mode on the transient response.
Findings
The proposed approach leads to more accurate results of displacement, velocity and acceleration when compared to the traditional finite element method.
Originality/value
In this paper, the application of the adaptive GFEM to the transient analysis of bars and trusses is presented for the first time. A methodology of identification of the preponderant modes to be retained in the modal matrix is proposed to improve the quality of the solution. The examples showed that the method has a strong potential to solve dynamic analysis problems, as the approach had already proved to be efficient in the modal analysis of different framed structures. A simple way to perform h-refinement of truss elements to obtain reference solutions for dynamic problems is also proposed.
O Método dos Elementos Finitos (MEF), embora amplamente utilizado como um método de solução aproximada, possui algumas limitações quando aplicado na análise dinâmica. Como alternativa para melhorar a resposta dinâmica da estrutura, o Método dos Elementos Finitos Generalizados (MEFG) pode ser usado para enriquecer o espaço de aproximação com funções apropriadas de acordo com o problema em estudo. Uma vez que a literatura mostra que o MEFG é um método eficaz na análise dinâmica, o presente trabalho tem como objetivo analisar um procedimento capaz de aumentar a precisão e eficiência computacional do método. Para tanto, a matriz modal, responsável pelo desacoplamento do sistema das equações de equilíbrio dinâmico, é utilizada com a presença apenas dos modos de vibração mais preponderantes do problema, que são identificados a partir de um proposto coeficiente capaz de indicar a influência de cada um desses modos. As análises foram feitas em elementos de barra e foi possível obter resultados transientes de deslocamento mais precisos, e mais eficientes computacionalmente.
Shear strength in reinforced concrete (RC) beams, especially in steel fiber reinforced concrete (SFRC) beams is a subject of great interest in structural engineering. In the case of beams without transverse reinforcement, the failure is explained based on a predefined crack pattern and kinematics, and the transfer of shear force accomplished through different mechanisms. Among these mechanisms, the aggregate interlock is present in most of the existing shear strength mechanical models in the literature, with divergences regarding its performance and preponderance. Thus, this paper focuses on evaluating the contribution of aggregate interlock throughout the critical crack formation process up to the ultimate load by performing bending tests on small-scale rectangular RC and SFRC beams without considering the effect of transverse reinforcement. The Digital Image Correlation (DIC) technique is used to track the patterns of shear cracks and their associated kinematics by measuring the relative displacements of opening (w) and sliding (δ). A detailed description of the shear behavior of these beams is provided by quantifying the aggregate interlock using the simplified Walraven model. The results help to understand the level of contribution of the aggregate interlock, and the main differences between structural elements of concrete with and without steel fibers in the scope of the shear strength.
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