Clap is a matlab routine that performs classical laminate analysis for any general anisotropic layup. The classical plate theory usually assumes that the material is isotropic, while a fiber reinforced composite laminate with multiple layers plies may have more complicated stressstrain relations. Input consists of ply material properties, material strengths, ply fiber orientation and stacking sequence, mechanical loads andor strains, and temperature and moisture loads. Classical lamination theory each lamina is orthotropic. An extension to classical lamination theory for use with. The method results in an explicit formulation that accommodates any throughthickness variation in the elastic, hygrothermal and piezoelectric properties of each layer. A usage document is also given to clearly delineate the purpose of the function. The most important lamination of classical lamination shell theory is that each ply is assumed to be in a state of plane stress and those transverse shear stresses were neglected.
To create a program in matlab that will calculate the stresses, strains, and curvature at any location of a polymer laminate comprised of multiple laminae arranged in a variety of orientations. We provide software for a variety of detail analysis procedures. Laminate effective material properties are tailored to meet performance requirements through the use of lamination theory integrated in the msc. Two separate instructional software resources are available. The classical lamination theory is used to develop these relationships. Classical laminate theory has been extensively used to describe the behavior of composite. The laminate is thin and is loaded only in its plane plane stress. Layered shells use classical lamination theory to model the structural. The failure analysis is performed using failure theories to evaluate first ply failure fpf load and last ply failure lpf load of the laminate which also specifies the mode of failure. Free excel software on composite laminate theory with added features. Each function is accompanied by a matlab test file to show usage. In classical laminate theory, the a, b, and d matrices collectively form the laminate stiffness matrix. Prediction of transverse directional strains and stresses of.
Improved classical laminate theory clt models are developed for plain weave, 5, and 8harness satin weave composites. Laminator is an engineering program written for windows 7, 8, and 10 that analyzes laminated composite plates according to classical laminated plate theory. Choose suitable failure criteria to check the strength of laminate at given load. Downloads aerospace engineering blogaerospace engineering blog. Simple straightsided untabbed tension and compression specimens. The modules are primary for composites, but some are also effective for metals. Motivation for this project was to develop an optimization tool for large composite panel design with the application to aircraft primary structures. Theories covered include thinplate classical lamination theory, first and thirdorder sheardeformable reissnermindlin, and reddy thick plates, and refined layerwise theories. Individual layer unit width classical lamination theory symmetric laminate panel flutter these keywords were added by machine and not by the authors. The four cornerstones of the lamination theory are the kinematic, constitutive, force resultant, and equilibrium equations. In classical lamination theory, the plate is assumed to have infinite dimensions and the whole. Finding stiffness matrices a, b, and d step 1 of 5 efunda. A clt analysis when midplane strains and curvatures are known sections 6. Summary of classical lamination theory clt calculations.
The program calculates a, b, d matrices as well as. The following assumptions are made in the classical lamination theory to develop the relationship. Altair esacomp is a software for analysis and design of composites. Macromechanics of a laminate usf college of engineering. The stresses obtained by ansys are compared with clt. Application of classical lamination theory and analytical. This paper proposes a method of deriving the engineering and strength properties of unidirectional lamina from laminate properties. The classical lamination theory predictions were in good agreement with the measured response of the pzt composite actuators and provide a useful design tool for these actuators. Plybased and laminatebased failure criteria are implemented. Finding stiffness matrices a, b, and d step 1 of 5.
Application of a classical lamination theory model to the. This process is experimental and the keywords may be updated as the learning algorithm improves. The classical plate theory usually assumes that the material is isotropic, while a fiber reinforced composite laminate with multiple layers plies may have more complicated stress. Laminate analysis program file exchange matlab central. Deriving composite lamina properties from laminate properties.
Classical lamination shell theory classical lamination shell theory clst is the simplest method used for the analysis of the shell structure. A line straight and perpendicular to the middle surface remains straight and perpendicular to the middle surface during deformation. The laminator is an engineering program written for windows 7, 8, and 10 that analyzes laminated composite plates according to classical laminated plate theory. Composite tutorial classical lamination theory altair. It is able to predict strains, displacements and curvatures that develop in a laminate as it is mechanically and thermally loaded. Composite laminate analysis spreadsheet an excel spreadsheet that calculates a, b, d matrices for any anisotropic composite laminate, and returns layer strains and stresses for defined membrane loads, bending moments, and thermal loads due to curing cooldown. Classical lamination theory an overview sciencedirect topics.
Reduction of thermal residual stresses of laminated polymer. Many references are available where classical lamination theory is utilized to describe composite material behavior. This paper presents the description of a webbased computer program for the analysis of laminated. Last time he ended with inplane laminate behavior, this time the outofplane behavior for the case of pure bending and membranebending coupling behavior are discussed.
A summary of classical lamination theory defining the laminate a laminate is an organized stack of unidirectional composite plies unidirectional meaning the plies have a single fiber direction rather than a weave pattern. Classical laminate theory models for woven fabric composites. Classical lamination theory matlab program objective. This calculator constructs the a, b and d matrices of a laminated fiberreinforced composite. Classical lamination theory clt extension of clt to stiffened panels margin of safety composite strength failure criteria linear buckling honeycomb panel failure stiffened panel failure composite joints coupling analytical methods with fea stiffened panel modeling approaches composite optimization. Classical laminate theory clt in his second lecture dr. Classical lamination theory clt is a commonly used predictive tool, which evolved in the 1960s, which makes it possible to analyze complex coupling effects that may occur in composite laminates. Laminate optimization netting analysis program lap. Summary of classical lamination theory clt calculations numerical examples illustrating discussion in. This software was first written in 1990 in quickbasic and since then has gone through several content additions and rewritten for new windows platforms. These models retain the simplicity of the fiber undulation model and the. Downloads aerospace engineering blogaerospace engineering.
The stack is defined by the fiber directions of each ply like this. Online software mats347 composites design and manufacture. Fea of composites classical lamination theory example 1 22. Dimitri soteropoulos revised by jacob wardell problem description. The classical lamination theory is almost identical to the classical plate theory, the only difference is in the material properties stressstrain relations. The laminate analysis program is a windows software tool for the analysis and design of. The latest version revised in 20 is available for windows xp and above. In classical lamination theory, the plate is assumed to have infinite dimensions and the whole panel undergoes the same thermal gradients.
By using the classical lamination theory clt and considering the coupling effect of tension and bending, an analytical model of stiffness prediction was developed for composite laminates with in. Classical lamination theory an overview sciencedirect. This repo contains matlab code for classical lamination theory. Its scope ranges from conceptual and preliminary design of layered composite structures to advanced analyses that are applicable for the final verification of a design. Hi is there any tutorials abut stiffness matrices for composite laminate a, b, d, because i used laminate tool. Results were compared to a commercially available unimorphtype actuator made from layers of metal, adhesive, and piezoelectric material. Fea of composites classical lamination theory example 1. Oct 12, 2017 composite tutorial classical lamination theory.
Composite analysis software laminate program esp composites. Elastic properties such as the the a, b, and d matrices are calculated. Introduction chapter 2 and 3 focused on the behaviour of a single layer. Abd matrices and abd inverse matrices helius composite. An extension to classical lamination theory is presented for the improved analysis of thin to moderately thick functionally graded plates. A summary of classical lamination theory william a. Laminate theory 12 the stressstrain relations in coordinates aligned with the principal material directions i. Ansys as a tool to perform fea and failure analysis of hybrid. Classical lamination theory matlab program dylan saracco. Graduate course descriptions structural engineering. Solution methods covered include exact, approximate ritz, galerkin and the finite element method. Sagemath open source mathematical software prime numbers and the riemann hypothesis papers books talks courses students the 20 jenks prize for excellence in software engineering applied to computer algebra student projects the modular forms database the lfunctions, modular forms, and friends database computer hardware software sage. The laminate stiffness matrix is used to express laminate resultant forces per unit width n and laminate resultant moments per unit width m in terms of laminate midplane strains e 0 and laminate midplane curvatures k. Please enter the layout information the angle of fibers of each layer of your laminate and click next.
In the final step, in order to quantify the nanoadditives effects on thermal residual stresses, the classical lamination theory and the energy method were used to calculate macro and micro thermal residual stresses in carbon fiberreinforced composite containing low weight contents of mwcnts. The laminator classical analysis of composite laminates unitn. Kassapoglou continues the discussion about classical laminated plate theory. The thermomechanical properties of such a layer can be predicted, and the stressstrain relationship is known. This matrix defines an orthotropic material which is fundamental in the. New fea tools tackle composite challenges machine design. The software is a library of matlab functions that can be used by students to write matlab programs for lamina and laminate analysis. All software has been updated to be consistent with the book. A four layer 090s graphiteepoxy composite laminate subjected to an axial load is considered figure 1.