In my case, my tomcat server work with TextWebSocketHandler.
Before doing this, you need to check this, supportsPartialMessages.
First of all, override supportsPartialMessages() as below.
//This value set as true in my properties file. Just for test. actually you don't need this.
@Value("#{config['server.supportsPartialMessages']}")
private boolean supportsPartialMessages;
//If you need to handle partial message, should return true.
@Override
public boolean supportsPartialMessages() {
    return supportsPartialMessages;     
}
And then I add "messageRoom" attribute to store partial message to each websocket session when connection is established.
@Override
public void afterConnectionEstablished(WebSocketSession session) throws Exception {
    super.afterConnectionEstablished(session);
    //I think this is easier to keep each message and each client.
    session.getAttributes().put("messageRoom", new StringBuilder(session.getTextMessageSizeLimit()));
}
When you get message from client, do this.
@Override
public void handleTextMessage(WebSocketSession session, TextMessage message) throws Exception {
    super.handleTextMessage(session, message);
    StringBuilder sbTemp = (StringBuilder)session.getAttributes().get("messageRoom");
    //isLast() will tell you this is last chunk or not.
    if(message.isLast() == false) {     
        sbTemp.append(Payload);
    }else {
        if(sbTemp.length() != 0) {          
            sbTemp.append(Payload);     
            this.logger.info(session.getRemoteAddress() + ":RECEIVE_TO[CLIENT][PARTIAL][" + sbTemp.length() + "]:" + sbTemp.toString());
            doYourWork(session, sbTemp.toString());
            //Release memory would be nice.
            sbTemp.setLength(0);
            sbTemp.trimToSize();
        }else {         
            this.logger.info(session.getRemoteAddress() + ":RECEIVE_TO[CLIENT][WHOLE]:" + message.getPayload());
            doYourWork(session, Payload);
        }
    }
}
This is done a few years ago, so I can't remember where I got this.
But I still appreciate to them.