A new functional perturbation method for linear non-homogeneous materials

Altus, Eli; Proskura, Aleksey; Givli, Sefi

doi:10.1016/j.ijsolstr.2004.08.010

Cited by 7 publications

(3 citation statements)

References 22 publications

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“…As introduced in the introduction this method is capable of solving bending, strength and Eigenvalue problems as introduced here. It is also capable of solving vibration problems [17] and was used to solve boundary value problems of linear materials with non-homogeneous properties [5]. Of course using the FPM for solving much more complicated problems like plates, shells and structures are not trivial missions and are good for future research.…”

Section: Discussionmentioning

confidence: 99%

A novel application of the FPM to the buckling differential equation of non-uniform beams

Totry

Altus

Proskura

2008

Probabilistic Engineering Mechanics

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Section: Discussionmentioning

confidence: 99%

A novel application of the FPM to the buckling differential equation of non-uniform beams

Totry

Altus

Proskura

2008

Probabilistic Engineering Mechanics

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“…We can consider φ (0) = 0, φ (1) = −ũ ,x and φ (2) =ũ. First of all, we use two terms of Taylor expansion for u(x)…”

Section: Examplementioning

confidence: 99%

A new approximation method to solve boundary value problems by using functional perturbation concepts

Pourghanbar

Ranjbar

2018

B Soc Paran Mat

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Functional perturbation method (FPM) is presented for the solution of differential equations with boundary conditions. Some properties of FPM are utilized to reduce the differential equation with variable coefficients to the equations with constant coefficients. The FPM can be applied directly for many types of differential equations. The exact solution is obtained by only the first term of the Frechet series for polynomial cases. Four examples are included to demonstrate the method.

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“…Their study identified an optimal ratio between the radius in the middle of the cylinder and the radius at the end for maximum carrying load capacity. Altus et al [2005] introduced a new method for obtaining the buckling load analytically for linear inhomogeneous materials using the functional perturbation method (FPM). According to them, this method provided more accurate results for linear inhomogeneous materials than the conventional Galerkin and Rayleigh-Ritz methods.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2014

J. Mech. Mater. Struct.

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Buckling is an instability encountered in a wide variety of problems, both in engineering and biology. Almost all engineering structures are designed with adequate safety factors to prevent failure due to buckling, yielding or dynamic loads. In a classical sense, design for buckling is done by carefully controlling the modulus of elasticity, moment of inertia and the length of the structure. Further, such an approach assumes the material to be homogeneous and does not generally account for the microstructural details of the column. In this paper, we study the buckling of inhomogeneous columns with a two-phase checkerboard microstructure. Monte Carlo simulations are used to generate microstructures with arbitrary volume fractions and phase contrasts (ratio of the modulus of individual phases). An analytical form is obtained for the ensemble averaged critical buckling load based on the results of over 18,000 eigenvalue problems at arbitrary volume fractions, phase contrasts and distributions. Further, microstructural realizations that correspond to the highest buckling load (best design) and the lowest buckling load (worst design) are identified and the corresponding distribution of individual phases is determined. Finally, the statistical nature of the critical buckling load is discussed by computing the statistical moments that include the mean and coefficient of variation.

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A new functional perturbation method for linear non-homogeneous materials

Cited by 7 publications

References 22 publications

A novel application of the FPM to the buckling differential equation of non-uniform beams

A novel application of the FPM to the buckling differential equation of non-uniform beams

A new approximation method to solve boundary value problems by using functional perturbation concepts

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