Prosedur Elemen-Hingga Multi Lapis Untuk Analisis Linear Elastis Struktur Beton Bertulang = Multilayer Finite Element Procedure for Linear Elastic Analysis of Reinforced Concrete Structure - Perpustakaan UGM, i-lib ([Yogyakarta] : Lembaga Penelitian dan Pangabdian kepada Masyarakat, Universitas Gadjah Mada, 1999)
ABSTRACT In 3-D Finite Element analysis for reinforced concrete structure, mechanical behavior modelling of material becomes a big challenge to be solved since concrete and reinforcement behavior are complicated. Several finite element modelling procedures have been proposed, among them is Layering Procedure, which was proposed by Hand et all in 1972. Deformations and stresses developed segmentally over the thickness of the structure have been considered in the model. In this procedure, each concrete layer was idealized as a flat shell element, considering deformations translational (u, v, and w) and rotational (a and t9y) degrees of freedom. Each steel layer was modelled as membrane element with translational (u and v) degrees of freedom. Idealizing the element as a flat shell was aimed to count for transverse shear stresses as the real condition. Constraint equations involved in translation deformations (u, v, and w) of any adjacent nodes in vertical direction have been introduced for satisfying the compatibility between the layers. Analytical study of the procedure in linear elastic condition and its numerical simulations intended to find out the step-by-step development of finite element equations or formulas suitable for the problem considered, the role of constraint equations in computation, and the advantages and disadvantages of the procedure. The displacement functions used was cubic polynomial for isoparametric quadrilateral 8 nodes element. Validation have been done by modelling the problem using 8 nodes solid elements. The results of this study included: stiffness matrices for Mindlin Plate and membrane elements in closed form, and constraint matrix that had form and size depending on the number and kind of layer's material in stack. The numerical simulations with concrete and reinforced concrete clamped-free structure's models, under flexure and torsion, indicated the abilities of the procedure for the purpose as meant. The shell elements considered had capability of representing more displacement degrees of freedom.