On Critical Buckling Loads Of Euler Columns With Elastic End Restraints

I n recent years, a great number of analytical approximate solution techniques have been introduced to find a solution to the nonlinear problems that arised in applied sciences. One of these methods is the homotopy analysis method HAM . HAM has been successfully applied to various kinds of nonlinear differential equations. In this paper, HAM is applied to find buckling loads of Euler columns with elastic end restraints. The critical buckling loads obtained by using HAM are compared with the exact analytic solutions in the literature. Perfect match of the results veries that HAM can be used as an efficient, powerfull and accurate tool for buckling analysis of Euler columns with elastic end restraint

An approximation of deflection line function at the rod loaded by buckling under self-weight

Rad se bavi aproksimacijom točne funkcije linije otklona za štap opterećen izvijanjem zbog vlastite težine pomoću funkcije, što je najbolje prikazano točnim oblikom ovog štapa. U ovom radu predlažemo metode derivacije kritične duljine izvijanja pomoću točnog rješenja i pomoću metode energije. Za zamjenske funkcije linije otklona su izabrane varijante goniometrijskih funkcija i polinomi. Pojedinačni koeficijenti funkcija su izabrani na temelju postojećih rubnih uvjeta i u slučaju nedovoljnog broja, oni su izabrani kako bi se izrazio točan oblik linije otklona štapa na najprikladniji način, koji je prenesen iz konkretnog primjera rješenja pomoću softvera SolidWorks. Rad prikazuje pogreške kritičnog izračuna duljine izvijanja nasuprot točnom rješenju, kao i maksimalna apsolutna i relativna odstupanja kod bočnog pomicanja za odabranu funkciju. Od pojedinačnih zamjenskih funkcija je naknadno izabrana ona koja ispunjava uvjet za opće korištenje i ima najmanja odstupanja od točnog rješenja.The paper deals with an approximation of the exact deflection line function at a rod loaded by self-weight buckling via the function, which is best-presented by the exact shape of this rod. In this paper, we suggest the methods of derivation of the critical buckling length by the exact solution and by the energy method. For the substitute functions of deflection line, the variants of goniometric functions and polynomials are chosen. Individual coefficients of the functions are chosen on the basis of existing boundary conditions and in the case of their insufficient count, they are chosen in order to express the exact rod deflection line shape in the most suitable way, which was transposed from the concrete example solution by SolidWorks Simulation software. The paper shows the errors of critical buckling length calculation against the exact solution, as well as the maximum absolute and relative deviations in the lateral displacement for the chosen function. From the individual substitute functions, one function that meets the condition for general use and has the lowest deviations from the exact solution, is subsequently chosen

The homotopy analysis method for q-difference equations

AbstractThe q-difference equations are kind of important problems in q-calculus and applied mathematics. In this paper, the homotopy analysis method is extended to find approximate solution for some of q-differential equations. The q-diffusion equation and some examples are analytically investigated. The series solutions obtained by the proposed method are checked by reducing the solutions of q-calculus problems to h-calculus approximate solutions when q→1

Research in structural and solid mechanics, 1982

Advances in structural and solid mechanics, including solution procedures and the physical investigation of structural responses are discussed

Advances in Vibration Analysis Research

Vibrations are extremely important in all areas of human activities, for all sciences, technologies and industrial applications. Sometimes these Vibrations are useful but other times they are undesirable. In any case, understanding and analysis of vibrations are crucial. This book reports on the state of the art research and development findings on this very broad matter through 22 original and innovative research studies exhibiting various investigation directions. The present book is a result of contributions of experts from international scientific community working in different aspects of vibration analysis. The text is addressed not only to researchers, but also to professional engineers, students and other experts in a variety of disciplines, both academic and industrial seeking to gain a better understanding of what has been done in the field recently, and what kind of open problems are in this area

Research in Structures, Structural Dynamics and Materials, 1990

The Structural Dynamics and Materials (SDM) Conference was held on April 2 to 4, 1990 in Long Beach, California. This publication is a compilation of presentations of the work-in-progress sessions and does not contain papers from the regular sessions since those papers are published by AIAA in the conference proceedings

NASA thesaurus. Volume 2: Access vocabulary

The access vocabulary, which is essentially a permuted index, provides access to any word or number in authorized postable and nonpostable terms. Additional entries include postable and nonpostable terms, other word entries and pseudo-multiword terms that are permutations of words that contain words within words. The access vocabulary contains almost 42,000 entries that give increased access to the hierarchies in Volume 1 - Hierarchical Listing