• Structural Engineering and Mechanics
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• v.90 no.1
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• pp.83-96
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• 2024

This paper suggests an analytical approach to investigate the free vibration and stability of functionally graded (FG) beams with both perfect and imperfect characteristics using a quasi-3D higher-order shear deformation theory (HSDT) with stretching effect. The study specifically focuses on FG beams resting on variable elastic foundations. In contrast to other shear deformation theories, this particular theory employs only four unknown functions instead of five. Moreover, this theory satisfies the boundary conditions of zero tension on the beam surfaces and facilitates hyperbolic distributions of transverse shear stresses without the necessity of shear correction factors. The elastic medium in consideration assumes the presence of two parameters, specifically Winkler-Pasternak foundations. The Winkler parameter exhibits variable variations in the longitudinal direction, including linear, parabolic, sinusoidal, cosine, exponential, and uniform, while the Pasternak parameter remains constant. The effective material characteristics of the functionally graded (FG) beam are assumed to follow a straightforward power-law distribution along the thickness direction. Additionally, the investigation of porosity includes the consideration of four different types of porosity distribution patterns, allowing for a comprehensive examination of its influence on the behavior of the beam. Using the virtual work principle, equations of motion are derived and solved analytically using Navier's method for simply supported FG beams. The accuracy is verified through comparisons with literature results. Parametric studies explore the impact of different parameters on free vibration and buckling behavior, demonstrating the theory's correctness and simplicity.

• Structural Engineering and Mechanics
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• v.89 no.3
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• pp.225-238
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• 2024

In this paper, a quasi-3D hyperbolic shear deformation theory for the bending responses of a functionally graded (FG) porous micro-beam is based on a modified couple stress theory requiring only one material length scale parameter that can capture the size influence. The model proposed accounts for both shear and normal deformation effects through an illustrative variation of all displacements across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the micro-beam. The effective material properties of the functionally graded micro-beam are assumed to vary in the thickness direction and are estimated using the homogenization method of power law distribution, which is modified to approximate the porous material properties with even and uneven distributions of porosity phases. The equilibrium equations are obtained using the virtual work principle and solved using Navier's technique. The validity of the derived formulation is established by comparing it with the ones available in the literature. Numerical examples are presented to investigate the influences of the power law index, material length scale parameter, beam thickness, and shear and normal deformation effects on the mechanical characteristics of the FG micro-beam. The results demonstrate that the inclusion of the size effects increases the microbeams stiffness, which consequently leads to a reduction in deflections. In contrast, the shear and normal deformation effects are just the opposite.

• Journal of the Korea Concrete Institute
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• v.14 no.3
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• pp.382-391
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• 2002

This study is devoted to the problems of thermal and shrinkage stresses in order to avoid cracking at early ages. The early-age damage induced by volume change has great influence on the long-term structural performance of the concrete structures such as its durability and serviceability To solve this complex problem, the computer programs for analysis of thermal and shrinkage stresses were developed. In these procedures, numerous material models are needed and the realistic numerical models have been developed and validated by comparison with relevant experimental results in order to solve practical problems. A framework has been established for formulation of material models and analysis with 3-D finite element method. After the analysis of the temperature, moisture and degree of hydration field in hardening concrete structure, the stress development is determined by incremental structural formulation derived from the principle of virtual work. In this study, the stress development is related to thermal and shrinkage deformation, and resulting stress relaxation due to the effect of early-age creep. From the experimental and numerical results it is found that the early-age creep p)ays important role in evaluating the accurate stress state. The developed analysis program can be efficiently utilized as a useful tool to evaluate the thermal and shrinkage stresses and to find measures for avoiding detrimental cracking of concrete structures at early ages.