Composition Feature of the Element Tangent Stiffness Matrix of Geometrically Nonlinear 2D Frame Structures Geometri kai netiesini r mini konstrukcij 2D elemento tangentin s standumo matricos sudarymo ypatumai

The expressions of the finite element method tangent stiffness matrix of geometrically nonlinear constructions are not fully presented in publications. The matrixes of small displacements stiffness are usually presented only. To solve various problems of construction analysis or design and to specify the mode of the real deflection of construction, it is necessary to have a fully described tangent matrix analytical expression. This paper presents a technique of tangent stiffness matrix generation using discrete body total potential energy stationary conditions considering geometrically nonlinear 2D frame element taking account of interelement interaction forces only. The obtained vector-function derivative of internal forces considering nodal displacements is the tangent stiffness matrix. The analytical expressions having nodal displacements of matrixes forming the content of the 2D frame construction element tangent stiffness matrix are presented in the article. The suggested methodology has been checked making symbolical calculations in the medium of MatLAB calculation complex. The analytical expression of the stiffness matrix has been obtained. Article in Lithuanian Geometri kai netiesini konstrukcij baigtini element metodo tangentini matric komponen i analitin s i rai kos n ra i samiai pateiktos literatūroje. Da niausiai pateikiamos tik ma poslinki standumo matricos. Tad sprend iant vairius konstrukcij analiz s bei projektavimo u davinius ir norint kuo tiksliau apra yti konstrukcijos tikr j tempt j deformuot būv , būtina tur ti visi kai apra yt tangentin s matricos analitin i rai k . iame straipsnyje nagrin jama geometri kai netiesinio 2D r minio elemento tangentin s standumo matricos sudarymo metodika naudojantis diskretizuoto kūno pilnutin s potencin s energijos stacionarumo s lygomis vertinant tik tarpelemetines s veikos j gas. Gautos vidini j g vektoriaus-funkcijos i vestin pagal mazginius poslinkius ir yra tangentin standumo matrica. Pateiktos r min s konstrukcijos 2D elemento tangentin standumo matric sudaran i matric analitin s i rai kos, i reik tos mazginiais poslinkiais. Siūloma metodika buvo patikrinta atliekant simbolinius skai iavimus MatLAB skai iavimo komplekso terp je. Gauta analitin tangentin s standumo matricos i rai ka. Straipsnis lietuvi kalba