FEMOD1 - 1D Finite Element Code

FEMOD1 is an interactive program for the setup, solution, and printout of a two point boundary value problem in a one dimensional region. The finite element method is used.

The differential equation has the form:

-d/dX ( K(X) dU/dX ) + C(X) * dU/dX + B(X) * U = F(X) + P(X)

The boundary conditions at the end points may have one of the following forms:

• U(X0) = value1;
• K(X0) * dU/dX(X0) = value1 * U(X0) + value2.

At run time, the user may interactively specify

• the extent of the region;
• the arrangement of nodes;
• the order of each element;
• formulas for the material functions K, C, B and F;
• the location and strength of the point loads P;
• the boundary conditions.

Reference:

Eric Becker, Graham Carey, J Tinsley Oden,
Finite Elements, An Introduction, Volume I.
Prentice-Hall, Englewood Cliffs, New Jersey, 1981.

Files you may copy include:

• femod1.f90, the source code;
• linear.inp, linear element input;
• linear.out, linear element output;

The list of routines includes:

• FEMOD1 is a one-dimensional interactive finite element program.
• BC_APPLY modifies the global arrays to account for boundary conditions.
• BC_READ reads the boundary conditions from the user.
• BC_WRITE prints the boundary conditions.
• C_CAP capitalizes a single character.
• C_EQI is a case insensitive comparison of two characters for equality.
• C_TO_DIGIT returns the integer value of a base 10 digit.
• COMRPN can translate formulas you type in and evaluate them.
• DIGIT_TO_C returns the character representation of a decimal digit.
• EKF_ADD adds the element arrays to the global arrays.
• EKF_SET computes the local stiffness matrix EK, and force vector EF.
• EKF_WRITE writes out an element stiffness matrix and right hand side.
• ELEMENT_READ reads the element data.
• ELEMENT_WRITE prints out information about the elements.
• ERROR_WRITE prints the RMS and energy norm errors.
• EXACT_READ reads formulas for the exact solution U(x) and dU/dx.
• EXACT_WRITE prints the formulas for the exact solution U and its derivative.
• FUNSCL evaluates a scalar function of one or more scalar arguments.
• FUNVAL evaluates a function given an argument and an RPN formula.
• GAUSS_READ reads the desired quadrature rule order.
• GAUSS_SET sets the weights and abscissas for Gaussian quadrature.
• GAUSS_WRITE prints out information about the quadrature rule.
• GKF_ASSEMBLE forms the global stiffness matrix GK and force vector GF.
• GKF_WIDTH computes the bandwidth of the stiffness matrix.
• GKF_WRITE prints out the global stiffness matrix and force vector.
• HELLO prints out an introductory message.
• HELP prints out a list of legal commands.
• I_GCF finds the greatest common factor of I and J.
• I_TO_S_ZERO converts an integer to a string, with zero padding.
• INICOM initializes data for COMRPN.
• INIFEM initializes the finite element data.
• LCM computes the least common multiple of two integers.
• MALPHA returns .TRUE. if STRING contains only alphabetic characters.
• MATERIAL_EVALUATE evaluates the material function formulas.
• MATERIAL_READ reads the material function formulas.
• MATERIAL_WRITE prints the material function formulas.
• MATWRT prints out a scalar, vector or array.
• NODE_READ sets the X coordinates of the nodes.
• NODE_WRITE prints out the location of the nodes.
• PCHECK checks parentheses in a formula.
• POINT_READ gets the point load data.
• POINT_WRITE prints out the point load data.
• PREP does the preprocessing of the problem.
• PROC assembles the linear system and solves it.
• RPNCHK examines IRPN, looking for a complete RPN expression.
• RPNSET converts a formula that the user has typed into RPN format.
• RPNVAL evaluates a "complicated" RPN formula.
• S_BLANK_DELETE removes blanks from a string, left justifying the remainder.
• S_BLANKS_DELETE replaces consecutive blanks by one blank.
• S_CAP replaces any lowercase letters by uppercase ones in a string.
• S_EQI is a case insensitive comparison of two strings for equality.
• S_INDEXI is a case-insensitive INDEX function.
• S_TO_R reads a real number from a string.
• SGB_CHECK checks the dimensions of a general band matrix.
• SGB_FA factors a matrix stored in LINPACK general band storage.
• SGB_SL solves a system factored by SGB_FA.
• SHAPE evaluates the shape functions at the local coordinate XI.
• SOLUTION_EVALUATE evaluates the solution U(X) and its derivative dUdX.
• SOLUTION_WRITE prints out the computed solution.
• SYMADD adds a new symbol name to the list of symbolic names.
• SYMLST prints out information about a variable.
• SYMVAL evaluates, sets or deletes a variable.
• TOKENS converts a character string into a list of token indices.

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