Critical load for buckling of solid wood elements with a high slenderness ratio determined based on elastica theory

Buckling tests were conducted using slender specimens of western hemlock. In the tests, the slenderness ratio was varied from 132 to 418 in which elastic buckling was induced, and the values of the critical load for buckling were obtained. When the deflection of the specimen was calculated from the loading-line displacement based on elastica theory, the value of deflection/load initially decreased because the compressive deformation was more dominant than the bending deformation. In contrast, when the load increased, the bending deformation became dominant, and the deflection/load-deflection relation exhibited linearity. These tendencies indicated that the transition from compression to bending was induced around the minimum value of the deflection/load. Therefore, it was recommended to determine the critical load for buckling using the load at the minimum value of the deflection/load where the deflection was calculated from the loading-line displacement.

Numerical Analysis of Large Deflections of a Flat Textile Structure with Variable Bending Rigidity and Verification of Results Using Fem Simulation

The paper presents the numerical modeling of large deflections of a flat textile structure subjected to a constant force acting on the free end. It was assumed that the examined structure is inextensible. The effect of the structure's own weight was also taken into account. In order to solve the problem, the flat textile structure was modeled using the heavy elastica theory. An important element of the analysis involves taking into account the variable bending rigidity of the examined textile structure along its length, which is often found in this type of products. The function of variable bending rigidity was assumed in advance. Numerical calculations were carried out in the Mathematica environment using the shooting method for the boundary value problem. The obtained results were verified using the finite element method.

Design, Modeling and Development of a Compliant Dual Resonator-Isolator

This paper investigates the construction, instrumentation, and dynamical modeling of a coupled three degrees of freedom compliant parallel arm mechanism. The compliant parallel arm, whose complete construction is carried out using 3D printing of polylactide (PLA) filaments, is a folded beam type mechanism, which is comprised of one primary and two secondary masses connected to two large deflecting beams. Dynamical model of the complete mechanism is obtained using Elastica Theory, where the large deflecting beams are considered as fixed-free cantilever beams subjected to a vertical tip load. Nonlinear load deflection curve, which is derived from the solutions of elliptical integrals, is approximated by a high-order polynomial function. Finally, the dynamics of the complete mechanism is derived using a classical lumped mass-spring-damper second order system. A linear actuator, PCB triaxial accelerometers, two laser displacement sensors and Arduino are utilized to gather acceleration and position information of each mass to identify the parameters of the lumped second order model using the offline Elastica Theory-based approach and polynomial fitting method. Numerical and experimental results verify the effectiveness of the proposed parameter identification schemes. Since system is nonlinear, state feedback linearization approach is adapted to linearize system equations at all operating points to control the trajectory of primary mass using a PID controller.

Mechanical design of buckled beams for low-stiffness elastic suspensions: Theory and application

Axially compressed buckled beams have been used for several decades as elastic suspensions characterized by high static stiffness and low dynamic stiffness. The most comprehensive mathematical modelling of buckled beams is based on the elastica theory, a rational framework that seeks the equilibrium configuration for arbitrarily large deflections and rotations. The use of the elastica model is straightforward for analysis purposes but is rather awkward for design tasks because it requires handling of elliptic functions. This paper presents approximate equations developed from the elastica solution to facilitate the structural synthesis of buckled-beam suspensions starting from high-level engineering specifications. The step-by-step design procedure is illustrated by means of a case study and the theoretical predictions are validated against test data and finite element results.

ANALISIS PERPINDAHAN NON LINIER BALOK BERDASARKAN TEORI ELASTIKA

ANALISIS PERPINDAHAN NON LINIER BALOK BERDASARKAN TEORI ELASTIKAAnalysis Displacement Non Linear of Beam Based with Theory of ElasticaAnwar Dolu1 & Amrinsyah Nasution21Jurusan Teknik Sipil Fakultas Teknik Universitas TadulakoAlamat korespondensi : Jl. Soekarno - Hatta KM. 9, Palu, Sulawesi Tengah, Indonesiaemail: [email protected] Teknik Sipil FTSL Instititut Teknologi BandungAlamat korespondensi : Jl. Ganesha No.10, Jawa Barat 40132email: [email protected] this study the authors analyze the nonlinear deflection on the cantilever with a load point P at the end . Analysis nonlinear deflection based on the elastica theory with solving elliptic integrals and method of iterations. For external load ( P ) is small ( P < 0.70 unit ) deflection less significant difference ( å < 5 % ) . For external load ( P ) increasing ( P > 0.70 unit ) , the difference is increasing the amount of deflection in significant. Deflection obtained by using the theory elastica smaller than the deflection by linear theory .Keywords : Nonlinear deflection , elastica theory , elliptic integrals , method of iterations , MAPLEAbstrakDalam kajian ini penulis menganalisis lendutan nonlinier pada tumpuan jepit bebas dengan beban titik P di ujung. Analisis lendutan nonlinier berdasarkan teori elastika dengan pemecahan integral elliptik dan metode iterasi. Untuk beban luar (P) yang kecil (P < 0.70 satuan) perbedaan lendutan kurang signifikan (å < 5%). Untuk beban luar (P) yang semakin meningkat (P > 0.70 satuan) maka perbedaan besaran lendutan semakin meningkat secara signifikan. Lendutan yang diperoleh dengan menggunakan teori elastika/nonlinier lebih kecil dibandingkan lendutan dengan berdasarkan pendekatan teori linier.Kata kunci: Lendutan Nonlinier, Teori Elastika, Integral elliptic,Metode Iterasi, MAPLE.