CN108984841A - Strength check under the calculating of composite laminated plate concrete moduli and specified load - Google Patents
Strength check under the calculating of composite laminated plate concrete moduli and specified load Download PDFInfo
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Abstract
Strength check the present invention relates to composite Materials Design field, under specifically a kind of composite laminated plate concrete moduli calculating and specified load.Include MIM message input module, computing module and message output module.Input material performance information, laying information and load data information in MIM message input module, calculation procedure can calculate three stiffness matrix A, D, B of composite laminated plate according to the input data, and calculate laminate concrete moduli and corresponding effective stiffness matrix of the pure loads in plane effect down and under simple bending torsion effect with D matrix according to A matrix.Whole strain and the deflection rate of laminate is calculated according to laminate stiffness matrix and load information simultaneously, it may further obtain the ess-strain information of each single layer, by using three kinds of Failure Analysis of Composite Materials criterion, to check whether the laminate meets intensity requirement under ordinance load effect.The present invention greatlys improve calculating speed, and can directly and quickly obtain ess-strain exact numerical solution for the laminated plate analysis in the case of simple stress, improves design efficiency.
Description
Technical Field
The invention relates to the field of structural design of composite materials, in particular to a checking program for calculating equivalent modulus and strength of a composite material laminated plate under a given load.
Background
As is known, in the finite element analysis process of a composite material, due to the complexity of the structure of the composite material and the anisotropy of the material, tedious input of ply information is often required when defining the material properties, and especially, when analyzing a composite material part with more plies or a more complex structure, a large amount of time and cost are required for giving the material properties. Because the symmetrical balanced ply composite material laminated plate has no stretch bending and stretch twisting coupling and has smaller stretch shearing coupling coefficient, the material attribute endowing process is simplified by an equivalent modulus method, the time cost is saved for the plane stress problem or the pure bend twisting problem, the design efficiency is improved, and higher calculation precision can be ensured.
At present, the strength analysis of the laminated plate bearing the in-plane tension-compression shearing force or the bending-torsion action is generally realized by using a finite element analysis method. When finite element software is used for calculation and analysis, concentrated stress larger than real stress is obtained at the load application position, which is not desirable for designers. The stress concentration makes the finite element analysis result not to correctly and intuitively reflect the stress condition of the laminated plate, and according to the Saint-Vietnam principle, the force is only a local effect and has no influence on the stress of the whole structure. The numerical solution can achieve high calculation precision when calculating the internal force of the laminated plate in the stressed state, input information is few, calculation efficiency is high, and the calculation result can reflect the integral stressed state of the laminated plate, so that the numerical solution is superior to finite element analysis for the problem.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a program for calculating the equivalent modulus and the strength of a composite material laminated plate under the action of a given load, which can calculate the equivalent modulus and the equivalent stiffness matrix of a symmetrical and balanced laminated plate, simplify the finite element analysis process, reduce the analysis complexity, improve the analysis efficiency, carry out high-efficiency numerical solution on the stress strain under the action of the in-plane load or the bending load borne by the laminated plate, adopt three common failure criteria to check the strength value of the laminated plate, and provide a design basis and basis for a designer to carry out the structural design of the composite material.
The technical scheme adopted by the invention for solving the technical problems is as follows: a composite material laminated plate equivalent modulus calculation and strength check under a given load comprises an information input module, an operation module and an information output module. After data is input and running, the calculation program firstly calculates the stiffness matrix of each single layer according to the data input in the information input module, and then integrates the stiffness matrix of the laminated plate according to the layering information. The equivalent modulus and the equivalent stiffness matrix of the laminated plate under the pure in-plane load effect and the pure bending load effect can be calculated through the stiffness matrix of the laminated plate, the total strain is obtained through combining the load information, the stress strain level of each single layer is further obtained through combining the layering information, and whether the laminated plate fails under the specified load effect is judged according to the maximum stress criterion, the Tsai-Hill failure criterion and the Tsai-Wu failure criterion.
Said is equal toThe information input module of the effective modulus and strength checking calculation program comprises three parts of material performance information, layering information and load data information: the material property information comprises the following contents: axial modulus E of the individual layers1Transverse modulus E2Poisson ratio mu12Shear modulus G12Axial tensile strength X of the individual layerstTransverse tensile Strength YtAxial compressive strength XcTransverse compressive strength YcThe shear strength S; the layering information comprises the following contents: the laying sequence ord, the thickness t and the laying angle theta of each single layer; the load data information comprises the following contents: axial tension and compression load Nd xTransverse tension and compression load Nd yIn-plane shear load Nd xyAxial bending load Md xTransverse bending load Md yTorsional load Md xy(the above loads are the internal force and the internal moment of force per unit width (or length) on the cross section of the laminated plate).
The equivalent modulus and strength check calculation program has the following calculation principle of an operation module:
step 1: according to the input data information E1、E2、μ12、G12And calculating the rigidity matrix Q of each single layer by using the formulas (2-1) to (2-3).
Wherein,
the equation (2-1) is written as a relation expressing stress in terms of strain:
where Q is a two-dimensional stiffness matrix, inverted by a two-dimensional compliance matrix S.
Step 2: the calculated single-layer stiffness matrix Q is used for calculating the integral stiffness matrix A, D, B of the laminated plate through formulas (2-4) - (2-9) by integrating the information of the stacking angle theta, the sequence ord and the thickness t.
The stress-strain relationship of the monolayer in the overall coordinate x-y at a ply angle θ is as follows:
wherein T is a coordinate transformation matrix.
Considering that the laminated plate is formed by laminating a plurality of single-layer plates, the stress-strain relationship of the k-th single layer is as follows:
for laminated plate have
In the formula, Kx、KyFor bending of the middle plane of the panel, KxyIs the plane torsion of the plate, epsilon0 x、ε0 x、 γ0 xyMid plane strain.
Let Nx、Ny、Nxy、Mx、Mx、MxyThe internal force and the internal force distance per unit width (or length) of the cross section of the laminated plate, the stress of the laminated plate and the internal force distance should satisfy the formula (1-9):
therefore, the relationship between the internal force, the internal moment and the strain of the laminated plate is converted into
Is abbreviated as
A laminate stiffness matrix A, D, B is obtained.
And step 3: according to the obtained A, D, B matrix, for the symmetrical balanced ply composite material laminated plate, no stretch bending coupling exists, so that the B matrix is a hollow matrix; due to A16、A26、 D16、D26The positive and negative alternative terms exist in the terms, so that the numerical value of the terms is much smaller than other rigidity coefficients, and the calculation can be simplified.
a. Under the condition of pure in-plane load, no bending load M exists, so that the relation between the internal force and the strain of the laminated plate is
N＝Aε0(2-10)
Thus, the equivalent modulus parameter E of the laminated plate can be obtained through calculation of the A matrix1、E2、 μ12、G12And an equivalent stiffness matrix Q.
b. Under the condition of pure bending load, no in-plane load N exists, so that the relation between the internal moment and the strain of the laminated plate is
M＝DK (2-11)
So that the equivalent modulus parameter E of the laminated plate can be obtained through calculation of the D matrix1W、E2W、 μ12W、G12WAnd an equivalent stiffness matrix QW。
And 4, step 4: according to the obtained A, D, B matrix and the specified external load Nd x、 Nd y、Nd xy、Md x、Md y、Md xyThe compliance relation formula of the internal force and the internal force distance expressing the strain and the curvature can be reversely deduced through the formulas (2-9) as follows:
therefore, the strain component of the whole laminated plate can be calculated, and then the strain components epsilon of different single layers can be obtained by using the formula (2-6)x、εx、γxyThen, the stress level sigma of each layer under the overall coordinate x-y and the main direction coordinate 1-2 can be obtained by the formula (2-4) and the stress conversion formulax、σy、τxy、σ1、σ2、τ12。
And 5: from the calculated stress level data σ in the principal direction1、σ2、τ12And respectively adopting the following three strength judgment criteria to carry out strength check on the composite laminated plate:
a. maximum stress criterion:
in the formula, Xt、YtFor tensile strength in the axial and transverse directions, Xc、YcCompressive strength in the axial and transverse directions, and shear strength.
Tsai-Hill failure criteria:
wherein X, Y corresponds to the axial and transverse strengths (the tensile and compressive determinations depend on whether the stress is positive or negative), respectively, and S is the shear strength.
Tsai-Wu failure criteria:
in the formula
F12Get
And judging whether each single layer fails according to each failure criterion, so as to obtain whether the composite material laminated plate meets the strength requirement under the action of the specified load.
The equivalent modulus and strength checking calculation program comprises the following information output by an information output module:
a. equivalent modulus E of the laminate under pure in-plane loading1、E2、μ12、G12And equivalent modulus E under pure bending and twisting load1W、E2W、μ12W、G12WAnd stiffness matrix Q, Q under both loadsW。
b. Main stress S of each layer material under the action of specified load11(i.e.,. sigma.)1)、S22(i.e.,. sigma.)2)、 S12(i.e.. tau.)12)；
c. And (3) checking the strength based on three composite material failure criteria, namely the strength based on the maximum stress criterion, the Tsai-Hill criterion and the Tsai-Wu criterion.
The method has the advantages that three composite material strength failure criteria are used for judging whether the laminated plate meets the strength condition, and the program is systematically combined with the composite material laminated plate equivalent modulus calculation program. The invention integrates the calculation method of the equivalent modulus of the composite material laminated plate and the strength check method of the laminated plate, and uses the computer language to compile a complete calculation program comprising three parts of input, operation and output, and a user can quickly obtain the equivalent modulus data and the strength check result of the composite material laminated plate only by keying in material parameters, layering information and load information at corresponding positions in an input module, thereby avoiding the complex processes of model drawing, grid division, analysis step establishment, boundary condition setting and the like in finite element analysis software, and the calculation result obtained by a numerical solution has higher precision.
Detailed Description
The invention is further described with reference to the following examples:
example 1: comprises an information input module, an operation module and an information output module. After data is input and running, the calculation program firstly calculates the stiffness matrix of each single layer according to the data input in the information input module, and then integrates the stiffness matrix of the laminated plate according to the layering information. The equivalent modulus and the equivalent stiffness matrix of the laminated plate under the pure in-plane load effect and the pure bending load effect can be calculated through the stiffness matrix of the laminated plate, the total strain is obtained through combining the load information, the stress strain level of each single layer is obtained through further combining the layering information, and whether the laminated plate fails under the specified load effect is judged according to the maximum stress criterion, the Tsai-Hill failure criterion and the Tsai-Wu failure criterion.
The information input module of the equivalent modulus and strength checking calculation program comprises three parts of material performance information, layering information and load data information: the material property information comprises the following contents: axial modulus E of the individual layers1Transverse modulus E2Poisson ratio mu12Shear modulus G12Axial tensile strength X of the individual layerstTransverse tensile Strength YtAxial compressive strength XcTransverse compressive strength YcThe shear strength S; the layering information comprises the following contents: the laying sequence ord, the thickness t and the laying angle theta of each single layer are sequenced from bottom to top according to the input sequence, namely the laying information of the first row corresponds to the first layer at the bottommost part of the laminated plate, the second row corresponds to the second layer, and so on, and the last row corresponds to the topmost layer; the load data information comprises the following contents: axial tension and compression load Nd xTransverse tension and compression load Nd yIn-plane shear load Nd xyAxial bending load Md xTransverse bending load Md yTorsional load Md xy(the upper load is the internal force and the internal moment per unit width (or length) of the cross section of the laminated plate).
And after the input module is set, the input module executes an operation program, sequentially and automatically calculates each single-layer rigidity matrix, the laminated plate integral rigidity matrix, the equivalent modulus, the integral strain and stress distribution and the strength check, and outputs the calculated result in a unified window.
The equivalent modulus and strength check calculation program has the following calculation principle of an operation module:
step 1: according to the input data information E1、E2、μ12、G12And calculating the rigidity matrix Q of each single layer by using the formulas (2-1) to (2-3).
Wherein,
the equation (2-1) is written as a relation expressing stress in terms of strain:
where Q is a two-dimensional stiffness matrix, inverted by a two-dimensional compliance matrix S.
Step 2: the calculated single-layer stiffness matrix Q is used for calculating the integral stiffness matrix A, D, B of the laminated plate through formulas (2-4) - (2-9) by integrating the information of the stacking angle theta, the sequence ord and the thickness t.
The stress-strain relationship of the monolayer in the overall coordinate x-y at a ply angle θ is as follows:
wherein T is a coordinate transformation matrix.
Considering that the laminated plate is formed by laminating a plurality of single-layer plates, the stress-strain relationship of the k-th single layer is as follows:
for laminated plate have
In the formula, Kx、KyFor bending of the middle plane of the panel, KxyIs the plane torsion of the plate, epsilon0 x、ε0 x、 γ0 xyMid plane strain.
Let Nx、Ny、Nxy、Mx、Mx、MxyThe internal force and the internal force distance per unit width (or length) of the cross section of the laminated plate, the stress of the laminated plate and the internal force distance should satisfy the formula (1-9):
therefore, the relationship between the internal force, the internal moment and the strain of the laminated plate is converted into
Is abbreviated as
A laminate stiffness matrix A, D, B is obtained.
And step 3: according to the obtained A, D, B matrix, for the symmetrical balanced ply composite laminate, no stretch-bending coupling exists, so the B matrix is an empty matrix; due to A16、A26、D16、 D26The positive and negative alternative terms exist in the terms, so that the numerical value of the terms is much smaller than other rigidity coefficients, and the calculation can be simplified.
a. Under the condition of pure in-plane load, no bending load M exists, so that the relation between the internal force and the strain of the laminated plate is
N＝Aε0(2-26)
Thus, the equivalent modulus parameter E of the laminated plate can be obtained through calculation of the A matrix1、E2、 μ12、G12And an equivalent stiffness matrix Q.
b. Under the condition of pure bending load, no in-plane load N exists, so that the relation between the internal moment and the strain of the laminated plate is
M＝DK (2-27)
So that the equivalent modulus parameter E of the laminated plate can be obtained through calculation of the D matrix1W、E2W、 μ12W、G12WAnd an equivalent stiffness matrix QW。
And 4, step 4: according to the obtained A, D, B matrix and the specified external load Nd x、 Nd y、Nd xy、Md x、Md y、Md xyThe compliance relation formula of the internal force and the internal force distance expressing the strain and the curvature can be reversely deduced through the formulas (2-9) as follows:
therefore, the strain component of the whole laminated plate can be calculated, and then the strain components epsilon of different single layers can be obtained by using the formula (2-6)x、εx、γxyThen, the stress level sigma of each layer under the overall coordinate x-y and the main direction coordinate 1-2 can be obtained by the formula (2-4) and the stress conversion formulax、σy、τxy、σ1、σ2、τ12。
And 5: from the calculated stress level data σ in the principal direction1、σ2、τ12And respectively adopting the following three strength judgment criteria to carry out strength check on the composite laminated plate:
a. maximum stress criterion:
in the formula, Xt、YtFor tensile strength in the axial and transverse directions, Xc、YcCompressive strength in the axial and transverse directions, and shear strength.
Tsai-Hill failure criteria:
wherein X, Y corresponds to the axial and transverse strengths (the tensile and compressive determinations depend on whether the stress is positive or negative), respectively, and S is the shear strength.
Tsai-Wu failure criteria:
in the formula
F12Get
And judging whether each single layer fails according to each failure criterion, so as to obtain whether the composite material laminated plate meets the strength requirement under the action of the specified load.
The equivalent modulus and strength checking calculation program comprises the following information output by an information output module:
a. equivalent modulus E of the laminate under pure in-plane loading1、E2、μ12、G12Or equivalent modulus E under pure bending and twisting load1W、E2W、μ12W、G12WAnd stiffness matrix Q or Q under both loadsW。
b. Main stress S of each layer material under the action of specified load11(i.e.,. sigma.)1)、S22(i.e.,. sigma.)2)、 S12(i.e.. tau.)12)；
c. And (3) checking the strength based on three composite material failure criteria, namely the strength based on the maximum stress criterion, the Tsai-Hill criterion and the Tsai-Wu criterion.
Example 2: on the basis of embodiment 1, in order to meet the condition that part of the requirements on structural rigidity are met, the method for increasing and outputting structural rigidity data comprises the following steps:
a. tensile stiffness EA:
wherein EA is the tensile stiffness, E is the elastic modulus, and A is the cross-sectional area; f is the tensile force, L is the rod length, Δ L is the rod elongation.
b. Bending stiffness EI:
wherein EI is bending rigidity, E is elastic modulus, and I is inertia moment of a section about a rotating shaft; f is the cantilever rod end concentrated force, l is the rod length, and omega is the rod end deflection.
c. Torsional stiffness GIp：
Wherein GIpFor torsional stiffness, G is the shear modulus, IpIs the polar moment of inertia; t is the torque, l is the rod length,is the relative twist angle.
It should be noted that the three structural rigidities described above represent the resistance to deformation of a simple unit area laminate, and do not take into account the cross-sectional shape of the actual product. In actual use, especially the torsional rigidity often needs to be considered as the cross-sectional structure of the product, so that the structural rigidity can be changed according to requirements in use.
Example 3: on the basis of the method in the embodiment 2, in order to facilitate the professional computer to check the calculation details, A, D, B matrix information is added, and the stress strain information sigma under the x-y coordinates and the 1-2 coordinates of each layer is addedx、σy、τxy、σ1、σ2、τ12. However, it should be noted that, due to the data type in the calculation process, only 4 bits after the decimal point are reserved for the short type, and therefore, correspondingly, data deviation occurs for the calculation result, and data 0 is often calculated to be 10-10Numbers below the order of magnitude.
Example 4: on the basis of the method in the embodiment 3, in order to more intuitively express the distribution situation of the stress of the laminated plate in the thickness direction, the output stress distribution information is added, wherein the output stress distribution information comprises axial stress, transverse stress and shear stress.
Example 5: on the basis of the description of embodiment 4, the small term A omitted in the stiffness matrices A and D16、A26、D16、D26And A11、D11With magnitude comparison therebetween, i.e. evaluationAnd converted into a percentage system, and the result is examined by A16、A26、D16、 D26Neglected rationality.
Claims (8)
1. The utility model provides a composite material laminate equivalent modulus calculates and intensity under the given load is checked which characterized in that: comprises an information input module, an operation module and an information output module; after data are input and run, the calculation program firstly calculates the stiffness matrix of each single layer according to the data input in the information input module, and then integrates the stiffness matrix of the laminated plate according to the layering information; the equivalent modulus and the equivalent stiffness matrix of the laminated plate under the pure in-plane load effect and the pure bending load effect can be calculated through the stiffness matrix of the laminated plate, the total strain is obtained through combining the load information, the stress strain level of each single layer is further obtained through combining the layering information, and whether the laminated plate fails under the specified load effect is judged according to the maximum stress criterion, the Tsai-Hill failure criterion and the Tsai-Wu failure criterion.
2. The composite material laminate of claim 1 having equivalent modulus calculation and strength verification under a given load, wherein the information input module includes information divided into material performance information, layup information and load data information; wherein the material performance information comprises the following contents: axial modulus E of the individual layers1Transverse modulus E2Poisson ratio mu12Shear modulus G12Axial tensile strength X of the individual layerstTransverse tensile Strength YtAxial compressive strength XcTransverse compressive strength YcThe shear strength S, the layering information comprises the contents: the laying sequence ord, the thickness t and the laying angle theta of each single layer, and the load data information comprises the following contents: axial tension and compression load Nd xTransverse tension and compression load Nd yIn-plane shear load Nd xyAxial bending load Md xTransverse bending load Md yTorsional load Md xy(ii) a The above loads are the internal force and the internal moment per unit width or length on the cross section of the laminated plate.
3. The composite laminate equivalent modulus calculation and strength check under a given load as claimed in claim 1, wherein the stiffness matrix Q of each single layer is calculated by using equations (1-1) to (1-3) based on the input data information;
wherein,
the equation (1-1) is written as a relation expressing stress in terms of strain:
where Q is a two-dimensional stiffness matrix, inverted by a two-dimensional compliance matrix S.
4. The composite material laminated plate equivalent modulus calculation and strength check under a given load according to claim 3, wherein the single-layer stiffness matrix Q obtained by calculation is integrated with the information of the stacking angle theta, the sequence ord and the thickness t, and the integral stiffness matrix A, D, B of the laminated plate is obtained by calculation through formulas (1-4) to (1-9);
the stress-strain relationship of the monolayer in the overall coordinate x-y at a ply angle θ is as follows:
wherein T is a coordinate transformation matrix;
considering that the laminated plate is formed by laminating a plurality of single-layer plates, the stress-strain relationship of the k-th single layer is as follows:
for laminated plate have
In the formula, Kx、KyFor bending of the middle plane of the panel, KxyIs the plane torsion of the plate, epsilon0 x、ε0 x、γ0 xyIs mid-plane strain;
let Nx、Ny、Nxy、Mx、Mx、MxyIs a unit width (or length) on the cross section of the laminated plate) The internal force and the internal force distance, the stress of the laminated plate and the internal force distance should satisfy the formula (1-7):
thus, the relationship of internal force, internal moment and strain of the laminate can be converted into
Is abbreviated as
A laminate stiffness matrix A, D, B is obtained.
5. The composite laminate panel equivalent modulus calculation and strength check at a given load of claim 4 wherein upon obtaining said A, D, B matrix, for a symmetrical balanced ply composite laminate there is no stretch-bending coupling so the B matrix is an empty matrix; due to A16、A26、D16、D26Positive and negative alternative terms exist in the terms, so that the numerical value of the terms is much smaller than other rigidity coefficients, and the calculation can be simplified;
a, under the condition of pure in-plane load, no bending load M exists, so that the relation between the internal force and the strain of the laminated plate is
N＝Aε0(1-10)
Thus, the equivalent modulus parameter E of the laminated plate can be obtained through calculation of the A matrix1、E2、μ12、G12And an equivalent stiffness matrix Q;
b, under the condition of pure bending and twisting load, no in-plane load N exists, so that the relation between the internal moment and the strain of the laminated plate is
M＝DK (1-11)
So that the equivalent modulus parameter E of the laminated plate can be obtained through calculation of the D matrix1W、E2W、μ12W、G12WAnd an equivalent stiffness matrix QW。
6. The composite laminate of claim 4 having equivalent modulus calculations and strength checks at a given load based on obtaining said A, D, B matrix and a specified external load Nd x、Nd y、Nd xy、Md x、Md y、Md xyThe compliance relation formula of the internal force and the internal force distance expressing strain and curvature can be reversely deduced through the formulas (1-9) as follows:
therefore, the strain component of the whole laminated plate can be calculated, and then the strain components epsilon of different single layers can be obtained by using the formula (1-6)x、εx、γxyThen, the stress level sigma of each layer under the overall coordinate x-y and the main direction coordinate 1-2 can be obtained by the formula (1-4) and the stress conversion formulax、σy、τxy、σ1、σ2、τ12。
7. Calculation of equivalent modulus and checking of strength under a given load for composite laminates according to claim 6, characterized in that said stress level data σ in the principal direction is calculated1、σ2、τ12And respectively adopting the following three strength judgment criteria to carry out strength check on the composite laminated plate:
a maximum stress criterion:
in the formula, Xt、YtFor tensile strength in the axial and transverse directions, Xc、YcIn the axial and transverse directionsCompressive strength, S is shear strength;
b Tsai-Hill failure criteria:
x, Y correspond to the axial and transverse strengths (the tensile and compressive determinations depend on whether the stress is tensile or compressive), respectively, and S is the shear strength;
c Tsai-Wu failure criteria:
in the formula
And judging whether each single layer fails according to each failure criterion, so as to obtain whether the composite material laminated plate meets the strength requirement under the action of the specified load.
8. The composite laminate equivalent modulus calculation and strength verification under a given load as claimed in claim 1, wherein said information output module outputs information comprising:
equivalent modulus E of a laminated plate under pure in-plane load1、E2、μ12、G12And equivalent modulus E under pure bending and twisting load1W、E2W、μ12W、G12WAnd equivalent stiffness matrix Q, Q under both loadsW；
B, a tension-shear stiffness matrix A, a bending-coupling stiffness matrix B and a bending-torsion stiffness matrix D of the laminated plate;
c main stress S of each layer material under the action of specified load11(i.e.,. sigma.)1)、S22(i.e.,. sigma.)2)、S12(i.e.. tau.)12)；
d, strength checking results based on three composite material failure criteria, namely the strength checking results based on the maximum stress criterion, the Tsai-Hill criterion and the Tsai-Wu criterion.
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| CN114218825A (en) * | 2021-11-30 | 2022-03-22 | 南京辰茂新材料科技有限公司 | Carbon fiber rod piece layering design optimization method |
| CN114297839A (en) * | 2021-12-23 | 2022-04-08 | 西安科为智通复合材料技术有限公司 | Method for designing and checking torsional rigidity of carbon fiber composite material winding pipe fitting |
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